Both are easy to propagate from cuttings. Try a mixture of potting compost and perlite, make sure you strip off leaves so that only bare stem is underground. I always cover cuttings with a clear plastic bag to stop them drying out. If you have hormone rooting powder you can dip the cut end into it before planting. Best done in the spring.
Normally Cordyline are pruned in spring. Very easy to do with a saw. Make sure you angle the cuts so that rain runs off. You will probably get babies growing below the cut. I believe yucca are similar.
We have what we think is a large yucca in our garden. DH cut off the side shoots and they re-grew well, but he can’t remember what time of year, sorry!
My cordyline has grown upwards into a tree with the shoots mostly intact as ‘branches’ but I have a yukka in the same situation as you it has grown a big old teenager or two and they are now overtaking my pathway so I too was wondering if I should just cut them off I ll look forward to answers also when s the right time of year to do it And can you grow them on ?
I have a large Cordyline plant in my garden border with two good sized off shoots. I don't want the plant to grow outwards preferring a straight growing plant. I know I can cut the side shoots off but am worried I may kill this lovely plant. Anyone have experience of cutting the off shoots off and when is the best time to do it.