The dates mentioned in this response are specific to Ohio and may or may not apply to your area.
According to an Ohio State University fact sheet, Clematis can be propagated by cuttings or layering. Cuttings should be "taken in May or June from half-hardened shoots of the current season's growth. Use a rooting mix of two parts sand and one part peat and a rooting hormone (available at garden centers). Supply high humidity, warmth, and light in order for the cuttings to root within four to five weeks. The large-flowered hybrids will take more time to root; if cuttings are taken in May, they may not root until late August. If rooted by early August, plant them out. If no rooting occurs until late August, hold plants over winter in pots and plant in early spring. Layering is the easier method and can be done in the fall. Choose a mature stem produced earlier in the season or from the previous season's growth. Secure it into the soil at the nodes or bury a pot containing a mixture of equal parts sand and peat. Secure the stem into the mixture. Rooting occurs within about 12 months at which point the rooted sections can be detached and planted."
To learn more about growing Clematis, consult the fact sheet Growing Clematis
Although Mandevilla can be propagated by layering or dividing the root-ball, most new plants are produced from softwood cuttings taken in early spring. As with most softwood cuttings, these must be kept in a closed propagation case or plastic bag until the roots form.
Check this link to learn more about propagating Mandevilla: http://www.botany.com/mandevilla.html
Also, here is a link to information about how to propagate plants by cuttings and layering: