Seeing how the moon controls a lot of the processes here on the earth, we may be better off leaving it alone and not messing with its mass. It would not be too long before we would be living on an iceball here and then it would matter little what precious metals, ores or whatever else we could gain from mining.
Thinking it was made of cheese got us this far. And this is definately one time when cutting the cheese might actually do more than produce a bad smell...