Does divorce occur if the husband says to his wife, "You are not under my responsibility," after he swore on the Qur'an to something he did not do?

Swearing on the Mushaf (copy of the Qur’an) is a binding oath. If the one who swore does the act he swore against, then expiation for an oath becomes incumbent upon him. As for a man's statement to his wife, "You are not under my responsibility (or in my charge)," this is a كناية (allusion/indirect statement) of divorce. If he intended divorce by it, then it takes effect; otherwise, it does not. If the divorce takes effect, he may reconcile with his wife before her waiting period (iddah) ends, provided this is not the third divorce. If it is the third divorce, then she becomes unlawful for him until she marries another husband with a valid marriage.