Is the husband's statement to his wife during an argument, "You want to leave, then leave; you want me to seriously relieve you of this...", considered a divorce, given that he was out of his mind?

Whatever issues from a person, be it divorce or anything else, without their full awareness, is considered ineffective. The words mentioned in the question are allusions (kinayat) by which divorce does not occur without intention, even if they were uttered in a state of full consciousness and complete awareness. Therefore, what transpired between you and your wife during the intense anger that caused you to lose your mind does not result in divorce. Indeed, it would not have resulted in divorce even if it had occurred in a state of consciousness, unless you had intended divorce by it. Anger is the key to evil. It is narrated on the authority of Abu Hurayrah (may Allah be pleased with him) that a man said to the Prophet (peace and blessings of Allah be upon him): "Advise me." He said: "Do not get angry." Narrated by Al-Bukhari.