Can you propagate this plant? How?

Two ways: after the little white flowers bloom in late summer, bright red berries will form. Take these off and squeeze the shiny black seed out of the red cover. Plant the seed (throw away the red pulp) and there you are! Germination is slow, but almost all the seeds will grow.
If your plant is in the house it may not flower and/or set fruit. In that case take the plant out of its pot and look at the place where the shoots come out of the ground. You can chop this lump into a couple of pieces (it is very very tough) and plant each to get two new plants. Be very careful in handling the plant. You don't really see them, but there are vicious little hooks along the stem that will cut you in mean little ways. Derek