How to Kill a Clematis?

I just ordered bare roots of a native clematis that I want to put in place of the non-native varieties I have. The company ships the bare roots in October. What is the most efficient (non-chemical) way to kill the existing vines to make way for the new?

Thanks for your help.

If you want to use the exact same spot for the new clematis, you'll probably have to dig it out. If you were planting a little bit away from the old ones, you could continually cut any old clematis foliage or shoots until it exhausts itself. Don't use salts or vinegars, etc to kill the old one as those products will contaminate the soil making it inhospitable for the new vines.
Would love to know what your native clematis is.

Thank you for the reply. The clematis is Clematis virginiana. Prairie Moon said its nickname is "Prairie Smoke on a Rope". I got a kick out of that. I do like the purple blossoms of the non-natives I have, but I have really been enjoying the butterflies and other bugs that natives are attracting. I have never seen any type of bug interested in our current vines.

I do not think I have enough space near the existing, since this needs the support. So I will probably dig them up.

C. virginiana reminds me of C. paniculata (I think the old name for autumn clematis?). I think you're right about the insects not being attracted so much to the showier clematis. Even the JBs aren't attracted. :)