Clematis put loads of energy into their seedheads. It also triggers a completion chemically in some species and hybrids. You can divert that energy and cancel the completion to some extent by deadheading.
The large flowered hybrids usually (depends on climate and other factors) benefit from a summer trim. It will promote a better late summer re-bloom. In some cases, it will promote a quick re-bloom. I've heard of someone with a long growing season who hacks back twice and gets a blooming flush 3 times each summer from some hybrids!

Seedheads of clematis tend to be as appealing to many growers as the flowers - they are great in arrangements, especially late season ones that can be left to dry. With the exception of some of the group II's that will produce a later summer rebloom, deadheading does NOT encourage additional blooming. And deadheading in that case has exactly the same effect as a light pruning after the first bloom flush.

Botanically speaking, flowering plants do not uniformly benefit or have a greater/extended flowering period if one deadheads spent flowers. This tends to be restricted primarily to annuals or single season plants that are genetically programmed to reproduce in a very short time frame. Deadheading eliminates or reduces seed production so the plant tries mightily to overcome this need for self perpetuation by producing more flowers that will hopefully mature into seeds. We humans have some how adopted the practice of deadheading and applied it to all plants thinking it will increase flowering when it is mostly a cosmetic effect. But perhaps the clearing away of spent flowers/removal of seedheads gives the appearance of allowing the plant to produce more flowers :-))