I have blackberries. At a blackberry trimming seminar I went to years ago they taught us on raspberry canes. They said they were the same a blackberrys. I am not sure if that is so or not--but here is what I learned about Blackberries.
At the end of the bearing season, cut out all the canes that bore. In the early
spring, cut back canes to a 3 or 4 foot height. Then cut all side leaders to about 12 inches or so.
how I got new plants was I bent over a piece of one of my plants so it touched the ground, and then covered it with dirt. when it had rooted, I cut it from the mother plant and then either left it where it was, or dug it up with a clump of surrounding dirt and replanted it where I wanted it to be. Just make sure the plant is well watered in both steps. early
spring is an excellent time to do this as it rains so often.