Stop watering as the foliage begins to wilt in late summer or early spring and allow the leaves to die down naturally. Too much water can cause the rue anemone roots to rot as the plant dies and enters dormancy.
Cut back the dead foliage after it dies back completely, removing it at the soil surface. Dispose of or compost the dead leaves. The foliage can harbor fungal organisms that attack the rue anemone when it reemerges in spring if it's left in the garden.
Cover the bed with a 1- to 2-inch layer of leaf mulch after cutting back. The leaf mulch shades the ground so the roots don't overheat and prevents the soil from drying completely. Decaying leaf mulch also emulates the rue anemone's natural environment and provides the plant with all the nutrients it needs for healthy growth.