Propagating clematis from cuttings is probably the least efficient/most difficult way of increasing or growing these plants but it can be done. Not sure if growth existant right now is ideal but sure won't hurt to give it a try.

Check out attached link for details.

Here is a link that might be useful: clematis from cuttings

I have 98% propagating success with laying. Take the longest vine you can find and scratch the surface next to a leaf bud and bury the section, cover with dirt and place something light weight on the area and forget about it for a couple months, but do make sure the area keeps moist. This time of the year is great for laying propagation.

Layering is the correct term. Agree, probably the easiest way.