The most common reason that Clematis leaves turn yellow is due to a magnesium deficiency. The solution, not surprisingly, is to get more magnesium to the plant. There are two ways this can be done:

1) Fertilize with a fertilizer that contains magnesium. Look for a fertilizer that is targeted towards tomatoes since many types of tomatoe fertilizers contain magnesium.

2) Use Epsom salts, they are a magnesium salt. Add one half teaspoon of the Epsom salts to one half gallon of water and mix it up. Water the plant with this solution, and it should perk back up.