Sedum spectabile and Sedum telephium and all the varieties from these species have much different root systems than the ground cover Sedum varieties and species. The tall border types have almost a carrot like root, consisting of one to several large fleshy taproots, and some to many small hair like roots attached either to the taproot or emerging from the crown of the plant at the soil surface. Here's how I propagate them.
First, dig up your clump - usually these grow with many stems coming from the main crown so dig around it with a sharp spade or shovel, then pull it out. Some of the clumps can be over a foot across, so they'll be heavy. This is a smaller clump of one of the hybrids I've been lucky enough to have volunteer from Sedum 'Purple Emperor'. I love the dark purple veining in the middle of the leaf.
You can pull the clump apart and decide how big to make them, making sure that each clump has at least one large taproot.
I pot them into four inch pots, as the large roots need lots of room. You can trim off any that are too big, to fit it in to the pot.
The stems can be cut into four inch lengths, each one with several leaves and these root within a week or two for good plug sized plants. I don't use any hormone or other special techniques, except that I use dry Sunshine Mix #4, and I don't water it for at least a couple of days to allow the cut surfaces to heal.