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Free electron laser powered by a solar array. Matter gets dug up and pulverized small by asteroid surface robots, squirted out as a dust stream, laser heated to plasma, charged by beaming electrons towards the catch-buckets. It flies through a large magnet (which keeps its position with ion thrusters), then coasts through vacuum, spreading out according to atomic content, falling into catch buckets and getting its charge neutralized.

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Well, you're not short on ideas.

Just visited European XFEL a few weeks ago. The linear accelerator was about 2km long and I believe the total cost of the laser is over 1 billion Euro, but nevertheless this is an awesome idea :)

Should be cheaper to build both of those sorts of things when the "making a vacuum" bit is already taken care of, and large amounts of space are available at no cost.

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