Now is certainly not an ideal time to move a clematis but you could if careful. However Sweet Autumn clematis is considered an invasive species in much of the eastern half of the country so I might rethink my choice of keeping it at all.

Invasive ? hmm...it took 2 years to grow a vine up my tree, and it doesn't seem to have overgrown at all, I'm in central Maryland.

https://www.invasive.org/alien/pubs/midatlantic/clte.htm

https://www.invasiveplantatlas.org/subject.html?sub=5354

https://www.marylandbiodiversity.com/view/3018

Invasive means that it spreads via seeds into wild areas, rather than any reflection on how it grows in your garden.

In my garden, zone 7 NC, it does spread like crazy from seeds. The little plants that result have very tough roots that are hard to get out. A big plant of it would be a royal pain to dig out I bet. I'd like to get rid of my big plant of it but really hadn't considered that I'd be able to accomplish it! The plant itself would be fine if it wasn't invasive. Where do you live, Hu? Possibly something about your climate or soil discourages the seedlings but I think my plant didn't spread so much for a few years.