Not unless you cut yourself...then it may hurt...lol. Just kidding.
Depending on how it's mounted, it might require removing the entire rock that it's attached to. If you're able to get to the base of the coral with an Xacto knive or razor knife of some kind, you could probably score the base a few times and then it should snap off right at the base. If it's small enough around, you could probably use some bone cutters to cut it at the base. If those aren't options, you can take the entire rock out and use a dremel tool to cut it off at the base.
Then you can use superglue gel to mount it somewhere else or to a small piece of rubble rock. While the rock is out, use a stiff toothbrush to remove as much of the algae as you can.