Hm, there should be one.

Make a slipcover.

How would that work with the tufting?

It wouldn't. You'll no longer see the tufting. They have iron on patches, but not sure how big they come.

Depends on how good you want it to look. If the cat is just going to go at it again, then patch it, slipcover it (secure the stuffing first). A professional reupholster is probably the only way to make it look "new". Not sure how expensive that would be, but you could probably email a photo and get a price from a few.