Yes, because it will help them bloom again, but when depends on when they bloom. Usually you prune them shortly after they have bloomed.
No, clematis vines should never be pruned back. I've had one for ten years, and have never pruned it, and it's doing spectacularly. Some things that you should do for them, however, is to make sure that they are fertilized, watered, and especially that they have lots of surface to climb and adhere to as they grow.
I've just made sure of that and the vine is doing great, and flowers profusely year after year.
I know most "experts" will answer this with "it depends on the type". Don't listen! Only prune off dead branches in the spring after you can see where the buds are forming on the live parts of the plant.
You will get more growth and more blooms! -joe.
Clematis should be pruned in February or March. Dead and/or weak stems. Topmost pair of large green buds.
A foot or more back from the stem tips. Group have the tendency to become bare at the base as they mature. The bare stems.
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