It really depends on the rock... Dense rocks are very difficult, you might need some type of hack saw to break up the rock... However, I had mushrooms growing on a large rock that was easily chiseled. I would take the rock out and put it in a separate container of water, I would wear rubber gloves because the mushrooms would slime, and i would use a hammer/chisel and fragging pliers to break off the pieces of rock behind the mushroom. Even if you end up accidentally ripping a mushroom (this would happen sometimes), every piece of flesh would end up growing into a new coral, I would just put the pieces back in my display and find new richordeas popping up.
Once removed, the stems of the mushrooms would still be attached to small pieces of rock, I would glue these to frag plugs and let the mushrooms recover. Once healthy again, I would give them to friends or to my LFS for store credit.
Bottom line.. From my experience, as long as it is not a dense rock and your rock is one of those sand/rubble concrete type rocks, if you cut the stone behind the stem of the mushroom, they are easily removable.
Also,
@ihavecrabs 's suggestion works as well. I have used both methods and when done right, it works well.