I don't think the mining company would be looking at high yield devices for
breaking up asteroids but low, perhaps part kiloton yields. Of course they
could send someone down to place lots of conventional charges like current
open cut mining practices.
Lasers could be used, use a much smaller array than a standard missile as
range does not have to be much. But until tractors come in you then still
have to gather and process all the chunks.
Perhaps the best would be a combination of explosives and then the vessel
attaches to the rock with one of those big wheel shovel things (whatever
they are called) and moves the shattered rock direct into the processors.
Antony