Question: I'm hosting a Minecraft server with 14 friends of mine playing on it. We peacefully build houses and structures, hold events, go kill the enderdragon, stuff like that. All is peaceful. Until one day, another friend of mine (let's call him "A") joined the server. Then our houses got griefed and burned. Our stuff is all gone. We (me, another owner, and 2 mods) took a month to investigate and finally found that "A" was griefing. We talked to him and told him not to grief again or else we'll kick him. And eventually we kicked him.

And now the problem begins. A moderator wrote to me saying that I should give "A" another chance, and that he apologized. So I thought, why not? Then, after I added him back -- on the very same day -- my best friend's house got filled with water. Checking the records, I found out that it was "A" again. I wanted to kick him, but it would hurt our friendship. I mean, we meet each other at school every day. He would be so mad at me. But if I don't kick him, 3 other players will leave the server.

What should I do to solve this mess?

Answer: 
It's always a bit tricky when you have a situation where real life and online life cross. Fundamentally, you have to decide which matters more, the real life situation or preventing the problems online.

If it is a friendship that you both value, then it may be worth having a chat with him offline about the behavior. Make sure he understands why it is a problem, that people, including you, don't like it and explain what the consequences will be. Get him to agree that he understands.

If he continues to do the behavior, follow through. You talked to him in real life and explained what would happen. He agreed to it and did it anyway. He doesn't have any right to be mad at that point. If he's willing to lie to your face, grief people, and then get upset about being removed, then he isn't really that good of a friend to begin with and probably isn't a big loss.

You could also consider allowing him back in eventually, but I'd suggest using increasing amounts of time that you don't let him back for, so he knows it will get more and more serious until hopefully his desire to spend time with you will offset his desire to cause trouble.
I think it is rather simple. You like this game, you enjoy playing it with other people.
Tell him that, if he values you as a friend, he will stop his behavior, if not just kick him.

People sometimes misses the real meaning of what is going on because they think is only an "online" event. But what if you were building real stuff, and he came and destroy it, would you accept that? What if you were writing a story on your computer, that is "virtual", would you like if he came and deleted it all?

You invest time in that game, is something you enjoy, the game is online, it may not be important, but your time and feelings are, if he can not accept/understand/respect that, do you think he will be able to understand in other contexts?

Value your time and feelings, and have friends that value them also.