I'd like to stick up for PaulS here. And that's despite the fact that he picks up my errors as well.
PaulS works very hard here - he answers many many questions, quite a few of which I look at and think "gosh this person hasn't tried very hard to help themselves". But usually PaulS answers with a hint or prod in the right direction.
After answering all these questions, every day, something really ridiculous like "can I run Minecraft?" probably blows a bit of a fuse. You may as well ask "can I run World of Warcraft?".
Google is your friend - everyone's friend (apart from privacy issues but that's another story). If you Google:
"minecraft server" +arduino
No results found for "minecraft server" +arduino.
So clearly the idea is a little unlikely to run. Plus a bit of research into how much RAM and disk a Minecraft server takes, compared to what the Arduino has, would help answer this for yourself.
It would be different if you were trying something like a "line follower robot", found heaps of hits on Google, but were having a bit of trouble getting it to work. And if you posted your circuit, and your code. Then you would expect a courteous and helpful response. And I expect PaulS would give you one.