Just cut with a knife or the like.
To attach to a rock, stick a toothpick through the leather, near what you want to be the base. Then, use a rubber band to secure the toothpick to the rock.
Cut the entire top off and then cut it into slices like a pizza. Glue a toothpick to a small rock and stick the coral on it so it is touching the rock. Put the coral in an area with decent flow and wait a week or two.
You can also just rip it apart with your hands as well, the thin parts tear pretty easily.