We just use a (clean) shovel- find a spot on the mother plant that will be easy to get to donor- it should have at least one mother stem and a decent sized (12 in) baby stem. Then place the shovel between the mother plant and donor plant and quickly and cleaning step on the shovel to separate them. Then dig the roots around the donor and pull it out. If I can get a root ball and not bother the roots too much, it is better.
As long as it has roots and some green stem/leaves, treat it like a plant. If it doesn't have roots, cut the stem and treat it like a rhizome (in a pot, little water until you see growth).

Makes since.