Drastic pruning is sometimes required. Just don't be afraid to take a chance. I'd say you cut the left side and not the right side, but once you get into a job like that you just might end up drinking and wishing I'd disappear.
Do whatever makes you feel comfortable.
This should alleviate your fears and bring a few chuckles as well. The main point being, "No one ever killed a clematis by pruning it".
http://hummingbirdfarm.net/cle...