"Hands are for helping, not hurting."
Let this be your mantra, over and over with him. Every single time he hits or is too rough with anything or anybody.
Daycare taught me this. They said it to all their children. Rome isn't built in a day with kids. They have to develop into learning to be gentle. And it's up to you to teach him. If he is not gentle, you remove him from who or what he isn't being gentle with and put him by himself as a time out.
I wouldn't have let him bury the bird, like Chacha said... And I would not just gloss over by saying "the bird went bye-bye". I would say firmly that we do not hurt animals. It's like making the point that he can't run across the street or touch a stove.
You really do need to make sure that your child doesn't hurt animals. I don't mean to imply that you have a bad child. I am telling you this because bad people sometimes start out hurting animals when they are young. Perhaps they don't have parents who care, or perhaps the parents just hide their heads in the sand where their kids are concerned. Don't be one of those parents. If you see behavior that concerns you, talk to the pediatrician and ask for help.
Sorry, but I disagree with the poster who said to have him take karate...