My supervisor seemed to be in a bad mood because he __________ when I asked if I could leave an hour early.

The sentence describes a situation where the supervisor appeared to be in a bad mood, as evidenced by his reaction to a request to leave work early. The blank requires an idiomatic expression meaning to respond angrily or to react with harsh words.

"Bit my head off" (Option D) is an idiom that means to shout at someone angrily or to respond with sudden irritation. It perfectly captures the supervisor's likely sharp or aggressive reaction to the employee's question about leaving early. 

The other options are either non-standard phrases or literal interpretations that don't fit the context: "Cut my voice" (Option A) suggests physically silencing someone, which doesn't apply here; "Ate my head" (Option B) is a nonsensical phrase in English; and "Hit my ear off" (Option C) implies physical violence, which is inappropriate for this workplace scenario.

Therefore, Option D is the only appropriate answer that aligns with both the context and grammatical correctness of the sentence.