Clematis pruning is ranked into three groups, depending on which season(s) they bloom and whether they bloom on old or new wood. Pruning is important because as they mature upwards, stems can become decrepit and produce fewer flowers.
As they mature upwards, the weight of the “canopy” can become too heavy for the supporting structure or lower stems to handle. Pruning back wilted or old stems increases air circulation preventing fungal diseases.
Check out this article (with images) from Fine Gardening on Pruning Clematis.