Cut a 4- to 6-inch long piece from the tip of an actively growing branch. Select a cutting with at least three leaves or buds and make the cut at a 45-degree angle above a leaf bud.
Strip the leaves from the lower half of the branch cutting.
Combine equal parts peat moss and perlite in a 6-inch diameter pot. Use a pot with a single bottom drainage hole. Water the medium until it's moistened but not soggy.
Dip the cut end of the daphne cutting in a rooting hormone, available from garden centers. Insert the lower third of the cutting into the potting medium until the cutting stands upright on its own.
Cover the pot with a clear plastic bag. Insert wooden skewers into the soil around the cutting to support the bag so the plastic doesn't touch the cutting.
Place the pot in a warm area that receives indirect sunlight. Water the potting medium if the surface begins to dry out.
Remove the plastic bag when the daphne has rooted and is producing new growth. Daphne shrubs typically take six to eight weeks to produce new roots.