Muslim apologists often complain that the Torah and Bible, while correct in the time of Muhammad, are now hopelessly corrupted, except for the parts about Muhammad. This is an innovation (AKA lie) of Islam and Muslims to hide the problem of Muhammad being ignorant of both the Torah and the Bible, along with false claims of Muhammad being in the Torah or Bible.
Muhammad and his Muslims had the Torah read to them:
Narrated Abu Huraira:
The people of the Book used to read the Torah in Hebrew and then explain it in Arabic to the Muslims.
Allah’s Messenger said (to the Muslims). “Do not believe the people of the Book, nor disbelieve them, but say, ‘We believe in Allah and whatever is revealed to us, and whatever is revealed to you.’ “
Sahih al-Bukhari 7362
Koran about Torah
Here are the verses of the Koran that are used to “justify” the charges of corruption in the Torah and Bible:
Do you covet [the hope, O believers], that they would believe for you while a party of them used to hear the words of Allāh and then distort it [i.e., the Torah] after they had understood it while they were knowing?
Koran 2:75
Notice carefully that they “used to hear the words of Allāh” and then “distort it”. This isn’t about distorting the text, but about speaking of the text.
And indeed, there is among them a party who alter the Scripture with their tongues so you may think it is from the Scripture, but it is not from the Scripture.
And they say, “This is from Allāh,” but it is not from Allāh.
And they speak untruth about Allāh while they know.
Koran 3:78
Notice “with their tongues” and “they speak untruth”. Again, it is about people lying and not speaking or reciting the text.
All food was lawful to the Children of Israel except what Israel [i.e., Jacob] had made unlawful to himself before the Torah was revealed.
Say, [O Muḥammad], “So bring the Torah and recite it, if you should be truthful.”
Koran 3:93
Note that the verse presumes that the written Torah is truthful, by Muhammad and Muhammad pretending to be Allah.
Among the Jews are those who distort words from their [proper] places [i.e., usages] and say, “We hear and disobey” and “Hear but be not heard” and “Rāʿinā,” twisting their tongues and defaming the religion.
Excerpt, Koran 4:46
Again note “twisting their tongues”. Again, it’s about speaking the text.
They distort words from their [proper] places [i.e., usages] and have forgotten a portion of that of which they were reminded.
Excerpt, Koran 5:13
Notice they “distort words” and have “forgotten a portion”. Again, speaking the text and deliberately omitting some of it.
O Messenger, let them not grieve you who hasten into disbelief of those who say, “We believe” with their mouths, but their hearts believe not, and from among the Jews.
[They are] avid listeners to falsehood, listening to another people who have not come to you.
They distort words beyond their [proper] places [i.e., usages], saying, “If you are given this, take it; but if you are not given it, then beware.”
Excerpt, Koran 5:41
Notice they “distort words”, which is speaking the text.
Indeed, those who inject deviation into Our verses are not concealed from Us. So, is he who is cast into the Fire better or he who comes secure on the Day of Resurrection? Do whatever you will; indeed, He is Seeing of what you do.
Koran 41:40
In this verse, “Us”, the demon, Jibril inside Muhammad, admits that others inject “deviation into Our verses”. That’s Muhammad admitting to the corruption of the Koran.
Bible
Note that the Koran has no verses about distortion or corruption in the Bible.
But, Infidel, what about Koran 2:79?
So woe to those who write the “scripture” with their own hands, then say, “This is from Allāh,” in order to exchange it for a small price. Woe to them for what their hands have written and woe to them for what they earn.
Koran 2:79
No one does this apart from Muslims. For example:

Obviously, none of this comes from Allah despite Muslims claiming: “This (Koran) is from Allah!”
This hadith confirms that the Gospel is not corrupted:
Amir b. Shahr said:
I was with the Negus when his son recited a verse of the Gospel. So I laughed. Thereupon he said: “Do you laugh at the word of Allah, the Exalted?”
Sunan Abi Dawud 4736
Explanation

The claim of corruption of the Torah comes from an incident where a Jew and a Jewess were caught in adultery, according to the Sahih hadith in Bukhari:
A Jew and a Jewess were brought to Allah’s Messenger on a charge of committing an illegal sexual intercourse.
The Prophet asked them. “What is the legal punishment (for this sin) in your Book (Torah)?”
They replied, “Our priests have innovated the punishment of blackening the faces with charcoal and Tajbiya [sic] {Lashing}.”
Abdullah bin Salam said, “O Allah’s Messenger, tell them to bring the Torah.”
The Torah was brought, and then one of the Jews put his hand over the Divine Verse of the Rajam (stoning to death) and started reading what preceded and what followed it.
On that, Ibn Salam said to the Jew, “Lift up your hand.”
Behold! The Divine Verse of the Rajam was under his hand.
So Allah’s Apostle ordered that the two (sinners) be stoned to death, and so they were stoned.
Ibn Umar added: “So both of them were stoned at the Balat and I saw the Jew sheltering the Jewess.”
Sahih al-Bukhari 6819
Notice: “one of the Jews put his hand over the Divine Verse of the Rajam (stoning to death) and started reading what preceded and what followed it.”

The Jews came to Allah’s Messenger and told him that a man and a woman from amongst them had committed illegal sexual intercourse.
Allah’s Messenger said to them, “What do you find in the Torah (old Testament) about the legal punishment of Ar-Rajm (stoning)?”
They replied, “(But) we announce their crime and lash them.”
Abdullah bin Salam said, “You are telling a lie; Torah contains the order of Rajm.”
They brought and opened the Torah and one of them solaced [sic] {so placed} his hand on the Verse of Rajm and read the verses preceding and following it.
Abdullah bin Salam said to him, “Lift your hand.”
When he lifted his hand, the Verse of Rajm was written there.
They said, “Muhammad has told the truth; the Torah has the Verse of Rajm.
The Prophet then gave the order that both of them should be stoned to death.
Abdullah bin Umar said, “I saw the man leaning over the woman to shelter her from the stones.”
Sahih al-Bukhari 3635
The Jews came to Allah’s Messenger and mentioned to him that a man and a lady among them had committed illegal sexual intercourse.
Allah’s Messenger said to them, “What do you find in the Torah regarding the Rajam?”
They replied, “We only disgrace and flog them with stripes.”
Abdullah bin Salam said to them, “You have told a lie the penalty of Rajam is in the Torah.”
They brought the Torah and opened it.
One of them put his hand over the verse of the Rajam and read what was before and after it.
Abdullah bin Salam said to him, “Lift up your hand.”
Where he lifted it there appeared the verse of the Rajam.
So they said, “O Muhammad! He has said the truth, the verse of the Rajam is in it (Torah).”
Then Allah’s Messenger ordered that the two persons (guilty of illegal sexual intercourse) be stoned to death, and so they were stoned, and I saw the man bending over the woman so as to protect her from the stones.
Sahih al-Bukhari 6841
Sahih Muslim:
Abdullah b. ‘Umar reported that a Jew and a Jewess were brought to Allah’s Messenger who had committed adultery.
Allah’s Messenger came to the Jews and said: “What do you find in Torah for one who commits adultery?”
They said: “We darken their faces and make them ride on the donkey with their faces turned to the opposite direction (and their backs touching each other), and then they are taken round (the city).”
He said: “Bring Torah if you are truthful.”
They brought it and recited it until when they came to the verse pertaining to stoning, the person who was reading placed his hand on the verse pertaining to stoning, and read (only that which was) between his hands and what was subsequent to that.
Abdullah b. Salim who was at that time with the Messenger of Allah said: “Command him (the reciter) to lift his hand.”
He lifted it and there was, underneath that, the verse pertaining to stoning.
Allah’s Messenger pronounced judgment about both of them and they were stoned.
Abdullah b. ‘Umar said: “I was one of those who stoned them, and I saw him (the Jew) protecting her (the Jewess) with his body.”
Sahih Muslim 1699a
Sunan Ibn Majah:
The Messenger of Allah passed by a Jew with a blackened face who had been flogged. He called them and said: “Is this the punishment for the adulterer that you find in your Book?”
They said: “Yes.”
Then he called one of their scholars and said: “I adjure you by Allah Who sent down the Tawrah (Torah) to Musa! Is this the punishment for the adulterer that you find in your Book?”
He said: “No; if you had not adjured me by Allah, I would not have told you. The punishment for the adulterer that we find in our Book is stoning, but many of our nobles were being stoned (because of the prevalence of adultery among them), so if we caught one of our nobles (committing adultery), we would let him go; but if we caught one of the weak among us, we would carry out the punishment on him. We said: ‘Come, let us agree upon something that we may impose on both noble and weak alike.’ So we agreed to blacken the face and whip them, instead of stoning.’
The Prophet “O Allah, I am the first of those who revive your command which they had killed off”, and he issued orders that (the man) be stoned.
Sunan Ibn Majah 2558
The Torah verse on stoning for adultery was concealed by the Jewish reciter of the Torah. This then leads to the claims of corruption by Muslim apologists, to cover for the fact that Muhammad was ignorant of the Torah and the Bible.
For more, see Koran – Confirms Scripture?
The people passed by the Messenger of Allah with a Jew who was blackened with charcoal and who was being flogged.
He called them and said: “Is this the prescribed punishment for a fornicator?”
They said: “Yes.”
He then called on a learned man among them and asked him: “I adjure you by Allah Who revealed the Torah to Moses, do you find this prescribed punishment for a fornicator in your divine Book?”
He said: “By Allah, no. If you had not adjured me about this, I should not have informed you. We find stoning to be prescribed punishment for a fornicator in our Divine Book. But it (fornication) became frequent in our people of rank; so when we seized a person of rank, we left him alone, and when we seized a weak person, we inflicted the prescribed punishment on him. So we said: ‘Come, let us agree on something which may be enforced equally on people of higher and lower rank. So we agreed to blacken the face of a criminal with charcoal, and flog him, and we abandoned stoning.'”
The Messenger of Allah then said: “O Allah, I am the first to give life to Thy command which they have killed.” So he commanded regarding him (the Jew) and he was stoned to death.
Allah Most High then sent down: “O Apostle, let not those who race one another into unbelief, make thee grieve…” up to “They say: If you are given this, take it, but if not, beware!….” up to “And if any do fail to judge by (the light of) what Allah hath revealed, they are (no better than) unbelievers,” about Jews, up to “And if any do fail to judge by (the right of) what Allah hath revealed, they are no better than) wrong-doers” about Jews: and revealed the verses up to “And if any do fail to judge by (the light of) what Allah hath revealed, they are (no better than) those who rebel.”
About this he said: “This whole verse was revealed about the infidels.”
Sunan Abi Dawud 4448
This hadith shows that some Koran verses were “sent down” in response to this incident. I think these verses are now in Koran 5:41-44. I believe the hadith copy of the Koran uses the Pickthall translation, not the Sahih International translation I use.
The charge of the Muslim apologists that the Torah and Bible are corrupt originated from here, with the Jews not applying the punishment of stoning to their people, and then Muhammad being helped to notice this conflict between Torah law and the less severe punishment by the Jews.
Another Opinion
Muhammad was a false prophet, for a false god, Allah, for a false religion, Islam, without even a false book, the Koran.
