Ideally spring is the best time to prune and take cuttings from your Yucca. You will need clean, sharp shears or secateurs to prune your plant.
Cuttings are best taken from mature wood. After you take the cutting, remove the lower leaves leaving a few leaves at the top. This will reduce moisture loss from the plant while it is growing new roots. Allow the cutting to dry out for a couple of days in a dry shady spot before potting up. Use Yates Potting Mix with Dynamic Lifter.
This will allow the roots to establish easily. In spring the cuttings will develop roots in about 4 weeks. You will need to stake the cuttings to prevent them from falling over. Once the cuttings have established a sufficient root ball, you can then plant them out in the spot where you choose.
This information is from the Yates Garden Guide: fully revised & updated 44th edition, HarperCollins, $39.99. You can have this information and so much more at your fingertips by purchasing the Yates Garden Guide, available at all leading bookstores and Bunnings stores.