A counterintuitive aspect of using the asteroid mass itself as propellant is that you want a LOW exhaust velocity. Not only does this maximize thrust for a given amount of power, it also conveniently gets rid of asteroid mass - so it takes even less energy to deflect what's left of the asteroid.
But for this, you'd rather not waste energy on vaporizing the rock. That's a lot of energy that basically gets you nowhere.
nyrath