Does anyone know if I can propagate Nandina Domestica like a bromeliad, banana or bamboo? Simply cut a piece from the root base with its root & replant? So if I have a small clump, can I cut out a piece & transplant?
Yes. Nandina (all varieties) can be propagated by root division. I would dig up part of the plant that includes a fat root with the finer root hairs and some stem and pot those pieces individually into gallon cans to grow them along, or else plant them directly into the location where you want them.
Take good care of them, their root has been compromised by being separated from the parent plant, and they may need to be in more shade for a while until they start growing more roots.
You can encourage the parent plant to put out more runners like this by pinching or cutting off several inches of the top, where the new growth is happening.