What do you think about this situation:
Bob divorces Mary not for fornication (she gets fat, or ugly, or burns the cornbread). Bob and Mary have three children and she has always been a housewife with limited education. She begs Bob not to leave her, He leaves her and their children anyway. Two years later, both having remained celibate, Bob now finds Judy and marries her. Now Mary, having remained celibate, can now "mentally" divorce Bob for fornication, and remarry scripturally, since God never accepted the first divorce which was not for fornication, and since God allows only the righteous to divorce the fornicator.
Essentially the point being asserted is that God only recognizes divorce done for the cause of fornication.
The general rule in the Scriptures is that a marriage lasts for the lifetime of both partners.
"For the woman who has a husband is bound by the law to her husband as long as he lives. But if the husband dies, she is released from the law of her husband. So then if, while her husband lives, she marries another man, she will be called an adulteress; but if her husband dies, she is free from that law, so that she is no adulteress, though she has married another man" (Romans 7:3-4)
"Now to the married I command, yet not I but the Lord: A wife is not to depart from her husband. But even if she does depart, let her remain unmarried or be reconciled to her husband. And a husband is not to divorce his wife" (I Corinthians 7:10-11).
It is this last verse that we want to focus on. Generally, a wife is not to leave her husband; however, if she does leave, she is to remain unmarried. The Greek word is agamos, which refers to an unmarried person, whether single, widowed, or divorced. It is well illustrated in I Corinthians 7:32-34, "But I want you to be without care. He who is unmarried cares for the things of the Lord--how he may please the Lord. But he who is married cares about the things of the world--how he may please his wife. There is a difference between a wife and a virgin. The unmarried woman cares about the things of the Lord, that she may be holy both in body and in spirit. But she who is married cares about the things of the world--how she may please her husband." Since "unmarried" is compared to one who has never married and contrasted to one who is married; it is, therefore, possible for a person to leave a marriage and enter a state of being unmarried. We call that "divorce" in the English language. A person in such a state is commanded to remain unmarried or to be reconciled.
In regards to divorce, Jesus stated, "And I say to you, whoever divorces his wife, except for sexual immorality, and marries another, commits adultery; and whoever marries her who is divorced commits adultery" (Matthew 19:9). Hence, a man can divorce his wife for some reason other than fornication ("sexual immorality" in this translation). Such a divorce would put him in an unmarried state, but it does not grant him the right to marry a different person. In your scenario, both Bob and Judy are now committing adultery by entering into a marriage to which they had no rights. However, Mary has not gained the right to remarry. The divorce from her husband was not for fornication. She cannot divorce him again because she is currently unmarried. Even if you want to call it "mental divorce" it does not exist.
It is unfortunate that Bob's sins have impacted her life, but such is the nature of sin. God does recognize that divorce occurred. It doesn't mean He likes it (Malachi 2:16), but you cannot conclude that it is not existent.