Help?

So Skyrim has been freezing up on me lately. Not surprising from a Bethesda game, but it seems to freeze up EVERY TIME the game autosaves, or close to every time. I've tried deleting most of my saves if it was a storage issue, but that didn't do a thing. I cleaned the disk more the once, and the inner circle where the disc connects to the case is a bit damaged, but the readable part of the disk seems fine. Can anyone give me a suggestion on what could rectify this issue? I play on xbox 360 btw.