Interestingly, here is a suggestion that TP propagation from cuttings is possible (in the second last paragraph). Has anyone tried it?
https://treesandshrubsonline.o...

I've heard of layering for peonies, trapping a stem with a leaf node removed against the ground and waiting for roots to form, but have heard it was very slow and not always successful, don't think most places in the states have long enough growing seasons to be successful. The cutting with humidity and bottom growth reminds me of s post I saw on FB years ago with a tp stem in water bottle with roots growing, no description was with it though

Liz, that's interesting.

This year, I had five new TPs in the pots that I planted late in October. Two of them came bare-root, so I knew they didn't have any feeder roots when I got them. I was surprised how many feeder roots they got in several months. I am assuming the feeder roots had started growing in late August or September. Thus, it might be possible to make them start growing their own roots if we take cuttings in late summer or early fall. Perhaps we should try it. I will prune a couple of branches from TPs and try next year, with God's help

It is possible

you can check this thread
https://tieba.baidu.com/p/5944...

or this video
https://youtu.be/BOPfpgQPUHs?t...

However I do not recommend people to propagate TP from cuttings, because the chance of growing root is not high(less than 60% in mass production according to some farmers in China), and even if it has roots comes out, it is still hard to survive in next summer, and even if it survived in next summer, it will take much longer time to bloom compare to a grafted plant(normally bloom next or 2nd year) because it will take at least 2 years to develop it's own root system without the help from a herbaceous peonies' nurse root.

But if you don't have any peony rootstock, or you have some cuttings left after grafting, or you just want some fun. You can try to keep them in wet sand, vermiculite, or peat moss. Some of them will grow some roots in a few weeks so you can plant them before winter.
Cover these cutting plants with soil during winter to prevent them from losing water, or plant them in pots and keep them in a safer place like your garage, if winter in your city is too cold. (low temperature lower than -5 C, or 23 F)
Don't expose these plants to direct strong sunlight next year, and you may get some new TPs with their own roots. It will grow very slowly in the first 2 or 3 years but you don't need to worry about the sucker. You may need to cut a few leaves before the first summer to have a balance between root and leaf.