.how do you remove the extractor from a mosin bolt?
As the old saying goes, "very carefully".
Often, there's old cosmoline stuck in there- so that needs to be checked first by GENTLY trying to pry the extractor away from the bolthead a tiny bit. If needed, I soak the bolthead in BrakeKleen.
I then set it along the edge of the bench (extractor hanging off the edge) and gently drive it out with a flat punch.