Clematis is fairly disease resistant, however clematis wilt can cause affected parts to droop and shrivel. Cut and destroy all affected parts. A more likely source of problems are soil, light or moisture conditions. Make sure the roots are planted in cool, moist soil with the foliage in full sun.
Clematis are relativly disease free but there are a few common dieseases they incur clematis wilt, mildew or more rarely slime flux. Slime flux is rare but untreatable. Mildew is treatable like with all plants.
Clematis are mostly prone to fungus disease. You may cut the stem to below the blackened area and treat the rest of the plant with a systemic fungicide.
If the new shoots turn brown and wilt, they are suffering from Clematis Wilt. Prune the shoots off and dispose of them. If aphids are attacking your plant, a strong spray with a hose will knock them off. Mildew can be lessened with pruning to allow more airflow.
Well I could give you a good answer for the question. However I have no clue what any of that is so I thought I would tell you that you might want to ask a Biology Major.