If you remove them later, the stump will be unsightly. Roll the buds out with your finger to keep from leaving scars on the stem. Leave the terminal bud on each stem tip. Each will develop a large, showy bloom. Cutting Cut flowers as soon as they fade so that seeds will not develop.
Seeds use up needed plant food.
When the foliage of garden peonies turns brown in the fall, cut the plants back to ground level. Burn the cut leaves and stems. Tree peonies usually are grafted on garden, or herbaceous, peonies and they will not overwinter if cut back to ground level. However, you must remove all shoots that grow from below the soil line. Otherwise, the plants will grow like garden varieties.