Red Yucca Hesperaloe parvifolia are truly not a Yucca at all. This plant is a succulent in the Agave family. The answer to your question: just about any time you are ready to tackle the job.
Succulents are a family of plants that can be transplanted anytime during the year. Ideally, the plant prefers to be transplanted in Spring or early Summer, when it is in a growth stage. If you have missed that window of time, and need to move or separate the Red Yucca, go ahead. Dig out away from the plant 6-8 inches and fairly deep as the plant has a good root structure and tap root. Don’t worry about not getting all of the roots. Retrieving 25% of the roots will be a successful move. As with all succulents, place the Yucca in a well drained soil or container. After transplanting water well to set the plant. Then water, or not, as you have normally done.
If the plant is large, wrap the plant with a rope or bungee cords to pull the plant in tight and minimize damage to the plant you the mover.
If the plant is large and needs to be separated, just take a sharp shovel and divide the plant into smaller ones. The separated plants can be easily potted up into containers pr planted. Always us containers that drains well.