Tree Peony Dying . When peony roots are exposed to air the fine filaments die within 15 minutes. Remove any stalks from the plant where the stem is damaged. Ask a Question forum Potted peony plant dying from garden.org Remove any stalks from the plant where the stem is damaged. Pruning is rarely necessary on tree peonies. I have a hanakisoi tree peony that's been in my garden for about 12 years.