How do you keep a sweater from unraveling?

I have this sweater that I want to alter. It's actually a men's sweater, so I'd like to change it up and make it cuter. I'm going for the oversized, destroyed sweater look that's so popular right now, but I'm afraid that if I cut it up it will unravel and be completely ruined. It's a fairly tight knit (no big holes between the threads) and it's not cheap thread either. Any ideas?