Scroll saw works best.
You can flip it and cut the back side with the saw like a dremel or diamond wheel and then cut the flesh with a new razor blade.
LPS really should be allowed to heal for 90 days after a saw cutting, but that is my 2cents on that matter. It really gives the tissue time to heal and regrow over the skeleton.
The reason the scroll saw works best is that it makes the finest cut and uses the least amount of friction heat. Rinse the cut with SW ASAP to remove the heavy coral skeleton sludge that forms from the sawing.(looks like drywall mud) This helps the flesh from being irritated or infections from forming.
Once the frags are made, let them heal in medium flow and light where they will not be picked at or disturbed.