Any clematis that is throwing up new shoots from the base is likely to be a group 3 for pruning which means, yes, you can cut back all the top growth down to those new shoots.
Give it a good feed of something like pelleted chicken manure and a good drink as clematis are hungry and thirsty plants. It will repay you with masses of flowers next summer.
Have a look at clematis viticella Etoile Violette. It may be what you have.