We are a few Muslims living in a non-Islamic country and facing a problem and need Fatwa on this problem. One of our friends and his wife had a quarrel over some matter and at their home and situation grew worse. His wife got angry and took a knife and put on her own neck and asked her husband divorce her. Her husband did not want to divorce and tried to avoid it, but she insisted and threatened to cut her neck if he did not. To avoid the bad situation her husband stated the divorce thrice, otherwise any wound to her could lead to a police case. Would you please tell us in this case divorce has happened or not according to Islamic Sharia.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

The divorce of a compelled person is null, i.e. not effective. The Prophet (Sallallahu Alaihi wa Sallam) said: "There is no divorce during enclosure" [ Abu Dawood and al-Syooti graded it as sound]. Enclosure means coercion.
The jurists have declared that any clear harm that could affect the body or wealth of the person, that of his wife, children, or parents if he does not divorce is considered as compulsion on divorce, and a divorce done under such threat is not valid.
In the given matter the wife threatened to kill herself if her husband does not divorce her; in this case the divorce was delivered only to save her life so it is not a valid divorce as long as the husband was sure that she was going to kill herself if he refused divorce, or he believed it strongly.
Allah knows best.