Ibew is right. Those are yuma ricordea and they drop babies like most mushrooms. They don't develop multiple mouths like Floridas do. Instead they will move a little and leave part of the base/foot in place which will separate and grow into a new yuma.
And if you do try to cut your yuma try to keep it underwater and only cut it if it is firm to the touch after you touch it to make it close up. If it becomes flabby and spits its guts probably best to let it reproduce on its own. Yo will probably end up killing it if you cut it.
Florida ricordias on the other hand you can take out of the water, cut them into 2-4 pieces and they will regrow, if your water parameters are in range.