BLUF: No safe way to remove&return slavers.
On any mission, there are "Removal checks" These can succeed which means the slaver is unaffected or fail which means the slaver is removed. Several traits and aspects modify the chance this happens, and I have no clue what the base chance is either. (I believe the base chance is modified by the mission-success rate, you can have slavers removed from successful missions, but it's far more likely that it'll happen with failed missions or critically failed mission.)
Once a slaver is removed, there's a second check to see if they return. The base chance of both checks seems tied with the "mission risk" fewer slavers return from Insane-risk missions than from run-of-the-mill missions. Several aspects also modify the return rate, however slavers tend to be gone for a long while.
The only solace I can offer is that wanted-posters in the city is also generated for slavers that will eventually return but is not currently part of the encampment.