Mining asteroids? Cause you always need more iron, carbon and silicates! Oh wait...
Do it the efficient way - the Asimov way. Take one large elemental furnace, place it near a bunch of oh-so-valuable rocks (heh). Use smaller craft - landing pods, whatever - to nudge the rocks towards the refinery. Rocks enter the processor and get split into their various (worthless) component elements, to be picked up later. Missing is impossible: you'd have to be a complete moron to compute the thrust wrong. None of this complicated manned landing-on or working-near dangerous asteroid fields. After boosting the rocks, the landing pods can be reused, no humans need go anywhere near it, and it can be totally automated. Course, you won't be building dick or squat out of ice, silicates and iron, but that never stopped HW2 mods right?

Using such a system, you could suck up your average maps worth of asteroids with a single refinery and perhaps a dozen utility vessels, so long as noone notices them. Why pick up little bits of rock when the laws of motion make it a simple matter to launch the whole rock into the refinery?
And Death Star? Mining tool? AHAHAHAHAHAHAHAHAHAHAHAHAHAHA. Deary me.