There are 3 categories of clematis for pruning purposes:
Spring bloomers, summer or fall bloomers and repeat bloomers. If you're not sure which you have, watch next seaso. It does sound, however, like you may have a summer bloomer. In any case, spring bloomers bloom on old wood from last year so, even though the plant can be severely pruned one needs to avoid cutting back the old, larger canes since that will provide the blooms next year. Your plant could be a spring bloomer.
Summer of fall bloomers grow blooms on the current years growth. They can be cut back severely (I cut mine back to about 12 inches to control the form of the plant) but should be done during dormancy. With repeat bloomers you should kinda watch the plant and see which bloom set (early or late) is the most prolific. If you like the early show, cut it back after that. You won't get much in the way of late blooms but next years spring bloom will be very nice. Or, conversely, if you have a more satisfactory late show... At any rate, for this class, don't prune it back too hard... more of a thinning to maintain habit.
Best of luck!