The best way that I have seen to deal with this is to kill them. You need two characters. One in a ship with dps and combat probes (t3d’s work well because of the bonus to prob launchers) and another can be anything, including a rookie ship.
Take the rookie ship and fly to the belt with the miners. When you are near create a bookmark (ctrl-b.) It needs to be about 1k-8k away so if it is not then try again. When you have that bm, warp to the belt and shoot at one of the npc’s. After about 7-10 seconds warp to the bookmark and start aligning away from the belt. The response fleet will show up in the belt, target and shoot at you. They should miss. The miners and any hauler they had will fly to a safe spot.
Use the scan/dps ship to find the miners and kill them all. There should be no response fleet at this spot. Miners from that npc corp will not respawn before the next downtime. You also get any ore/loot they drop as a bonus.
To do this with the Guristas and Blood miners you have to use a cloaky ship at the belt so you can set up before they respond. In this case you don’t need to shoot at the belt, they will chase you without it. There is a bug I have seen sometimes where they just sit there and do nothing though. This won’t help you if the roaming gang of 5 or so frigs decide to pay you a visit.