Many types of Clematis can be propagated by a technique called layering. Select 1-year-old stems with good buds. Cut a small slit along the stem. Pin the stem to the soil on the ground with a piece of wire or hold it down with a rock. Cover the slit stem with soil and keep it moist. Sever the stem when it has developed roots at the slit. You can dig up the rooted stem, clip it from the parent plant, and move it to a new area of the garden. See the following link for an illustration and description of layering and compound (serpentine) layering techniques.