The definition of bite someone’s head off is:
(verb) to be very angry with someone and reply rudely to them
A: Excuse me, may I sit in this seat?
B: No! My boyfriend is sitting there, idiot!
A: Oh, sorry! You don’t have to bite my head off.
The teacher bit the student’s head off when he answered his cellphone in class.
We had to complain to our manager when one of our co-workers was always biting our heads off if he was in a bad mood.