Here to be "cut off" means to be killed. Alternate translation: "For the whole family of Ahab will perish, and I will cause every male child in his family to be killed" or "Every member of Ahab's family will die, including every male child" (See: [[rc://en/ta/man/translate/figs-euphemism]])
This phrase is used to refer to every male, but it specifies "child" to emphasize that it includes children. Alternate translation: "every male" (See: [[rc://en/ta/man/translate/figs-synecdoche]])