Mother plant should be fine. Division will likely be fine as well.

I've done this before with a clematis growing at a long abandoned home.

It was planted very close to a tree and the area was choked with large tree roots I couldn't get even my smallest shovel past, so I had to settle for a small sprig of vine without much root attached.

The little baby has made it's second return this spring, so I'm thinking the transplant was a success.

A clematis propagation webpage I am fond of calls this process of separating a vine with a bit of root from the mother plant 'Nibbling'.

Here is a link that might be useful: Propagating Clematis

Thank you both for your feedback. I'm now very hopeful!!
I'll follow up in a month or two to let you know how it goes.