Because peonies are tender perennials that grow back every year, they won't need to be pruned like roses or shrubs. Unlike some roses, peonies bloom only on new stems, so the old stems don't need to remain overwinter. In fact, peonies tend to die back naturally during the fall and winter. Allow your peony plants to wilt naturally, leaving the foliage out for as long as possible to allow the roots to gather energy from the leaves for the coming blooming season. In the fall, cut the stems down to the ground to clean up the garden and deter insects and pests from hanging around.
While you can cut your peony plants all the way back at the end of the season, during the growing season you'll want to keep an eye out for damaged or diseased foliage and branches. Using a clean pair of scissors or clippers, cut away the damaged pieces. Of course, you can harvest blooms from your peonies during the growing season, too!