The President is generally considered a type II clematis, but it is treated as a type III in my garden here in NC. If the plant is completely finished blooming, why not trim back the plant by half, keep it watered and give it a good slow nitrogen fertilizer, and you might be rewarded by a bloom flush just as big as your initial spring flush later in the season.

If you wish to clip just the potential seedheads off, clip just behind where the flower head was attached to the stem. Clipping off the seedheads may or may not keep pruning group II clematis blooming however. Better to follow the advice given earlier for more blooms.