It seems to be common that peonies should be propagated by division, not by cuttings. However, I tried it anyway as I wrote before:
The cuttings looked strong for a while, but after two weeks they lost their vigour, and after three weeks they were dead.
Although it may depend on how you take the cuttings, I think that dividing is much a easier way to propagate peonies.
By the way, there is a green stem from the picture above, but it is not a peony. It is a sweet pea which was accidentally left in the soil and sprouted.