The method I use for fragging the majority of hard corals is primarily the same with the cutting tooling being an Inland band saw.
Cooling liquid used is fresh mixed saltwater with enough iodine to color it a light amber. This helps to disinfect cuts as they're made which has shown to greatly increase frag survival.
All corals are stored during cutting in a small bucket holding water taken directly from their home aquarium. This water is used both to keep them wet as well as for rinsing any flesh away from cuts while I'm working on them.
All finished, and rinsed, frags or trimmed colonies are soaked in Brightwell Aquatics Restor dip to insure that minimal flesh is lost.
Both soak buckets are rinsed and replenished between colonies to reduce the risk of interactions between loose flesh of different coral species.
Notes about Galaxea:
Galaxea is one of the easiest hard corals to frag due to the fact that it easily bounces back whether coralite boundaries are followed or not. For this reason, I like to cut colonies of galaxea into a grid of small squares.
As with most encrusting LPS corals, galaxea will exhibit growth more quickly if frags are cut as thin as possible. To do this I cut all frags down parallel to the living surface of the animal. While doing this, it's important not to cut into the portion of the skeleton that has color due to living flesh.
If there's a specific species of coral that you would like to see fragged, drop a comment below.