I've always cut them up like pizza, or taken slices out of the skirt of a larger one.... mouth or no mouth.. multiple mouthed ricordea can be separated into single ricordea with its own mouth by simply cutting them as such.
Ricordea can be removed on rocks, but the rock and way the ricordea is anchored makes a difference. For example, a ricordea on a smooth rock may be able to be removed with a credit card, or something plastic with a small flat end to pry with. If a ricordea is anchored in a rock, it is easier to hang the rock upside down(assuming you can remove it from the tank) and cut the entire head off with scissors via the foot.
After removal/propagation I recommend a little lugol's dip/tank water mix to help it heal.
hth