Does the Bible say anything about falsely accusing a woman of being a whore or prostitute?
One of the Old Testament laws was "You shall not bear false witness against your neighbor" (Exodus 20:16). Lying was never considered to be acceptable, regardless of what the lie was about.
I believe that you might be thinking about the passage dealing with a husband accusing his wife of not being a virgin when they married.
"If any man takes a wife and goes in to her and then turns against her, and charges her with shameful deeds and publicly defames her, and says, 'I took this woman, but when I came near her, I did not find her a virgin,' then the girl's father and her mother shall take and bring out the evidence of the girl's virginity to the elders of the city at the gate. The girl's father shall say to the elders, 'I gave my daughter to this man for a wife, but he turned against her; and behold, he has charged her with shameful deeds, saying, "I did not find your daughter a virgin." But this is the evidence of my daughter's virginity.' And they shall spread the garment before the elders of the city. So the elders of that city shall take the man and chastise him, and they shall fine him a hundred shekels of silver and give it to the girl's father, because he publicly defamed a virgin of Israel. And she shall remain his wife; he cannot divorce her all his days. But if this charge is true, that the girl was not found a virgin, then they shall bring out the girl to the doorway of her father's house, and the men of her city shall stone her to death because she has committed an act of folly in Israel by playing the harlot in her father's house; thus you shall purge the evil from among you" (Deuteronomy 22:13-21).
The implication of this law is that he was led to believe that she was a virgin prior to their marriage and then discovered that he had been lied to.
There was another law in Numbers 5:12-31 which deals with a man who suspects his wife was unfaithful to their marriage but had no evidence. The husband had the option to bring her before God. If God showed that she was unfaithful, despite her denial, she would receive a wasting disease from God. If it is shown that she had been faithful, then the husband's jealousy would be shown to be unfounded.