As NH reefer kid mentioned, the only thing living in that stalk is right up near the polyp. You could easily snap them off at the base, but then you'd have two separate stalks. It looks like they're joined and embedded in epoxy and I bet if you took a dremel or screwdriver to the "rock" you could chip it away from the base of the skeletons/stalks.
Could just be the picture, but it looks like they're getting blown around a bit. Just make sure you have them in gentle flow wherever you end up putting them.