>>16835716 (OP)
Realistically, you wouldn't.
The problem with rockets is weight. You need fuel to carry weight, and the fuel has weight, so you need more fuel to carry fuel. The part of the rocket that reaches space is like a tenth of the starting mass of the rocket.
What is an asteroid? Mass. You need fuel to get to the asteroid, then you need WAY more fuel to bring it back. And you need fuel to carry that fuel. And fuel to carry that fuel.
>but you're not bringing back the entire asteroid
Doesn't matter. You have to bring back quite a lot of material to make the trip worth it. Rocket launches are expensive. Sure you could bring back 20 kg of metal without significantly increasing fuel requirements, but those are the most expensive 20kg of metal ever produced. And that's ignoring the hardware and energy required to mine asteroids, which is pure sci-fi at the moment