snap (one's) head off
1. Literally, to force the head off of a person or animal with a sudden, forceful, violent motion. I stood horrified when he picked the poor animal up and snapped its head off. I remember being traumatized after seeing a movie as a kid where a giant snaps a man's head off.
2. To respond to someone with extreme and sudden anger. What's wrong with the boss today? I just tried to ask him a question, and he totally snapped my head off! The teacher snapped Billy's head off for talking during class again.
snap someone's head off
Fig. to speak very sharply to someone. (Based on snap at someone.) How rude! Don't snap my head off! Mary snapped Ted's head off because he had come in late.
bite/snap somebody’s ˈhead off
(informal) speak to somebody angrily without good reason: He was only making a suggestion — there’s no need to snap his head off!