What's up with that? That makes NO SENSE at all. Mining isn't about removing stuff from the asteroid, it's about having the stuff that you get from removing said stuff from asteroids. Why would they even care if you mined it before or after you got the mission? Or even if you just found it floating in space.
There shouldn't be a mining mission anyway, the mission should be: "Get me X tonns of Y, make sure it's not stolen. Mining is a good option."
If you happen to have something, and someone else wants it, why would they even bother to send you out and get the same something AGAIN? They wouldn't, they'd just ask you for what you have already, cause they don't want to wait, and you would get a nice bonus over selling it normally.
This is just yet another artificial and unlogical hurdle for players to do missions swiftly, and/or earn money.
When I used to do some mining, I would just go out, get whatever, return to the station, have a look at who wants my stuff at a higher price, and sell the rest. I guess that's not an option anymore. Not that I mine anymore, it's as boring as it gets. And frontier's RNG hates me anyway. 2 million per hour? I can get that much in a single trade run... Well I would if cAPI would be working.
God forbid someone make money mining