Is it OK to cut down peonies after blooming?

You can trim off the dead peony blooms, but leave the foliage intact. The plant needs all of its leaves to build up the blooms for next year. Similarly, you can cut off the bloom stalks of Stella d'Oro when a cycle of bloom is done. But don't cut back the foliage. 

You might consider planting a clematis with the peonies. The clematis can climb through the peony foliage for support and bloom in the same area later in the season.