Cut the stems down to one or two inches above the ground with pruning shears. This peony dies back with the first frost and regrows every year, so extreme pruning will not harm the plant in the long run.
Push a spade into the ground 6 inches from the stems, angling it toward the center of the plant and working in a circle to cut the roots. The circle will encompass most of the important roots.
Lift the plant out of the hole and place it on a tarp for transport.
Choose a new location for the fern leaf peony in full sun or dappled shade and fertile, moist, well-draining soil.
Dig a hole twice as wide as the root ball of the peony and to a depth the same height as the root ball. The extra width will give the plant a chance to grow strong, new roots in its new location.
Place the peony in its new hole and fill in with dirt around the root ball. Make sure the top of the root ball is even with soil level. Tamp the soil down to firm the plant in place.
Water the peony to a depth of six inches from the base of the plant out to the edge of the planting hole.
Place a 2-inch layer of mulch around the plant to protect its roots over the fist winter.