How do I delete data for one game in the iPad Game Center? I have one particular game that saves data through the game center. Somehow the saved game data got messed up which causes the game not to work properly when I a connected to the internet (I.e. When the game center is accessible). 

Is there some way to delete all the data belonging to that game only?
The simplest way is to delete the game from your iPad, which will destroy any local stored game data, and will prompt you to remove the app from Game Centre (which I assume you want to do if it's corrupt on the Server). Then redownload the app (or re-add it in iTunes in your computer). This should allow you to start with a clean slate.