The actor, 52, was forced to make a humiliating public apology last month after Amber Heard smuggled their dogs into Australia.
Appearing on "Jimmy Kimmel Live!", Depp said, "He looks somehow inbred with a tomato. It's not a criticism, I'm just saying, I was a little worried... He might explode."
Joyce has responded to the actor's tomato name-throwing by comparing himself to Hannibal Lecter.
"I think I'm turning into Johnny Depp's Hannibal Lecter, aren't I?" he said.