I have a very beautiful blooming clematis but it has been around for years. I am wondering if you can ever completely chop off all vines to just about 2 inches from the soil to give it a fresh new start with new growth right from the base,since the vine stocks have slowly sagged downward to the base of the vine over time.
Pruning does differ with Clematis varieties.
Here is an article that will help you with regular pruning.
I will tell you that I have also had some mature Clematis, varieties are unknown, that had also become a tangled mess and I needed to replace the trellis supports.
I trimmed them back to 12 to 18" in height. Although I had less flowers for a year or two, my vines are in much better shape and have recovered completely.
I find Clematis very hard and forgiving. I am in a zone 4 garden, so no pampering here!