If you want to cut them there are some things to consider.
1st the genus ricordia is suceptable to infection along the cut, conditions must be "streile" to be succesful, other corallamorphs are less likely to melt after cutting.
2nd You don't need to cut them, good light and the right feeding conditions they split by themselves fairly rapidly.
most people who frag any type of mushroom usually break the rock that they are on and then they have "2".
If you just want to take some off the rock, the way they are collected in the wild is with a flat tipped instrument, a flat chissel or I use a flat blade diving knife. I get right up to the base of the riccordia and with the blade flat against the rock I push quickly seperating the animal from the bottom. In a fish tank, I'm not sure if you can do this without hurting the animal, in the ocean the subtrate doesn't move, a rock in a tank or even if you remove the rock first will probably shift when you push, hurting or killing the animal if the blade slips.
If other people remove them from the rocks in their tanks, I would be interested so maybe I can find a better way of harvesting them in the wild.
Good Luck with whatever you try