Peonies die back to the ground in winter and put out new growth in the spring so the only pruning needed would be to remove injured or diseased stems or if one is crossing over another and rubbing together. Then when you do prune, cut the stem all the back to ground level. If you want bigger blooms then you do what's called 'disbudding' same thing that is done on fruit trees, remove smaller buds leaving one big one that the plant can concentrate all it's energy on. They absorb energy through their leaves so always leave as many as possible on the plant to promote good growth next year.
I cut the dead stalks down in the fall and remove them & dead leaves from the property to control botrytis blight.
IF they accidentally catch my eye on a late-fall-not-too-busy day, I remove the dead parts. IF not, early spring will do.
I let mine die back naturally and simply remove the dead leaves and stalks from the garden either late autumn or early winter.
