You can just use scissors or a razor blade and cut it off at the rock. It can be tricky to get it attached to something though (some people use string/fishing line on a needle and run it through the stalk once and tie it to a rock or frag plug).
It will all grow back if any is left behind though. I have cut the same pieces down numerous times in my tank, and it grows right back. May be able to put some kalk paste on what is left behind if you do not want it to grow back.
I like to use bone cutters and get a little piece of rock underneath. You can use a bit of superglue gel to attach it to a frag plug or attach elsewhere.
Sadly you can cut and pull it all you want all it takes is the smallest amount left behind and it will be back. I'd personal put as much of that rock in the sump and replace main display with new rock. Once it's mature remove the old stuff from the sump. Good luck happy reefing