Ask Mr. Smarty Plants

Jackie O'Keefe answered a previous question for Mr. Smarty Plants about dividing Hesperaloe parviflora. Here's what she wrote:

Hesperaloe parviflora (red yucca) is a real workhorse plant for dry landscapes. Its long-lasting and attractive blooms, wildlife value, easy-care nature and suitability to our climate and soils make it very desirable in our landscapes. Over time, as you have experienced, the clumps expand and become denser. Far from being a problem, this is an opportunity. These clumps are easily divided and the excess pieces can be moved to other sites, potted up, or given to your budding gardener friends. This solution is preferable to chopping away foliage, which can leave the plant with an unkempt look. 

To divide, a task best done in fall or winter before new growth starts, take a close look at your plant. You should be able to see where the clump has formed new offsets as it grew. These can be dug away with a sharp spade. Each offset will produce a new plant. If more drastic size reduction is necessary, you can dig out the root clump and divide the whole thing. This site, Grow'em Plant Propagation Database, Clump Division, is a good visual of the process. It should be noted that the visuals are of a daylily, Hemerocallis, while the Red Yucca, not a yucca at all nor a daylily, is a member of the Agavaceae (Century Plant) family. Dividing an overcrowded plant gives it growing room again.