They are surely mean compared to more docile fish. There is a bit of chasing when I get new fish, but it lets up after a day or two. However, the Picasso did kill a wrasse I introduced a few months ago. I just don't really add fish to my tank any more. The tank mates these guys have are two angels and two tangs and one clown. Everyone gets along pretty well. The blue-ish one is a Niger Trigger. Had him for seven years or so. He's a hand biter. It makes working in the tank pretty stressful, but I like a challenge[emoji3]
This should answer your biting question: