Praise be to Allah.
Cursing one’s wife is not permitted, and it is not a divorce; she still remains married to him and he has to repent to Allah for it and seek the forgiveness of the one whom he has cursed. Similarly, it is not permitted for him to curse his children or anyone else among the Muslims, because the Prophet (peace and blessings of Allah be upon him) said: “Trading insults with a Muslim is evildoing and fighting him is kufr (disbelief).” (authentic – agreed upon). And he (peace and blessings of Allah be upon him) said: “Cursing a believer is like killing him.” (al-Bukhari in his Saheeh).
These two saheeh hadeeths (authentic narrations) indicate that a Muslim’s cursing his brother is a major sin, so we must beware of it and restrain our tongues from committing this awful sin.
A woman is not divorced if her husband curses her; she is still married to her husband, as stated above.