Yes, I would confront someone cutting the lock on a board. Or a bike. Or anything, really. No, I wouldn't just walk up and punch them.
I would say something along the lines of "Ok man, if the board is yours, that's cool, but you just cut a lock and you're not walking away with that board until we get someone over here to get your info." Then, flag down ski patrol or really anyone who works there to check the guy's ID, pass, whatever, and make sure that if it's actually a stolen board, they have all of his info. If he was like "F*** tha,t I'm leaving" I'd probably let him go and report it immediately.
If he says it's his board is there some way for Patrol to confirm, or refute it on the spot?