Under the circumstances, I wouldn't know for a fact that that bike was stolen, so I wouldn't have done anything. If I saw the homeless dude sawing away on a locked bike, I might call the cops but nothing more. If I saw someone sawing away on my locked bike, I would walk up to him and say, "Thanks very much, but I have the key." If he turned and walked away, I would leave it at that. If he tried to get rough I would respond in kind. Keep in mind that the cops and courts take a VERY dim view of vigilante justice.