system
Given the following post, respond as if you're commenting on Reddit:
human
[General] If a race of people could mine asteroids how would they go about mining the ore while in 0G?

Edit: Also how would they Smelt the ore in 0G after the fact?
gpt
Fly in line with the asteroid so that both velocities match and cancel eachother out. Fire a remote mining station that latches on via harpoons. 

Attach the drill to the asteroid (via small drill) and use that connection instead of gravity. As you drill, you vaccume up the debris and sort through it in the safety of your own ship or station. 

Once finished, simply calculate when you want to disconnect and let go, allowing the mining station to be picked up by the ship that dropped it off.