Clematis wilt is a disease that can only be tackled by pruning out the disease.
If only leaves are affected, you can prune off the side shoots that have those leaves.
If the infection has gotten into the central stem/trunk, the stem/trunk must be cut down to ground level. Do not leave a stub above ground. As long as the roots are clean, they should be able to regenerate new growth.
Clean your clipper blades with alcohol if the blades contacted an infected part before cutting clean parts..