First things first
Do not attempt to frag zoanthids without eye protection and latex gloves. Zoanthids are posionous and can cause very bad eye irritaiton, blindness, even can put you in the hospital. You do not want to get their paly toxins in open wounds on your hands.
Assuming all that is ok, get a tweesers and a razor blade, use the tweezers to pull up the matt and use the razor to help separate the matt from the rock. If you have a sharp chisel the same can be used instead of the razor blade. It is imperative to get the matt up to create a good frag.
Be careful!