Snap Someone's Head Off Meaning

(idiomatic) To suddenly and sharply rebuke or insult a person, especially in response to a harmless remark.

Example: 1915, Kathleen Norris, The Story of Julia Page, ch. 5,
  "Pa's awfully cranky," Mrs. Cox said resignedly. "He's always been that way! You cook him corn beef—that's the night he wanted pork chops; sometimes he'll snap your head off if you speak."
1918, Kate Douglas Wiggin, The Story Of Waitstill Baxter, ch. 8,
  He won't have a pleasant morning, I can tell you! I shall snap his head off every time he speaks to me.