Don't worry about destroying the plant. Plants seem to be very forgiving. Just make sure there a bit of top growth with each root section. Of course, the sooner the divisions get into the ground the better. If it's not possible to accomplish this right away, hold them over for awhile by keeping their roots wet and the plants out of direct sun.
Cuttings work best for woody stemmed or creeping perennials.
Snip off 4- to five inch shoots. Remove lower leaflets and dip into rooting hormone. Insert the coated end of the cutting into potting soil, moisten, and cover with a plastic bag. Place the pot or tray in bright, indirect light. Inspect the cuttings every couple days and remove molding leaves and shoots.