Prune them hard. Leave like a foot of growth above ground. Invert a bucket or a plastic pot or similar contraption on top of the plant so that they don't get trampled over. Keep them well watered. Remove the buckets once the construction is over. Clematis are such hardy plants and they like the occasional hard pruning in my experience.

Excellent advice!! You must be prepared to sacrifice the bloom period to save the vines and the method described above should work beautifully. Hopefully the deck reconstruction will not take too long, as would be best to keep the vines covered for the shortest amount of time.

Make sure they do get watered as necessary under their protective caps :-) You might take this time to rethink your support system as well, to something that will coordinate with or compliment the rebuilt deck.

You could construct a "cage" from strong welded wire...the kind used for animal...to put over the drastically-pruned plants. The openings in the wire I'm thinking of can be 2"x4" or bigger. Cut five pieces of this wire and fix them together with zip-ties in an opened-bottomed box shape.

The wire panels you cut need to be big and tall enough, say 2' x 2' x 3' or so, that people will see and walk around them rather than tripping over, or stomping on, them. You may want to tie orange safety tape strips to flutter at the upper edges, too.

Once the cages are over the clematis stubs, use something similar to tent stakes to hold the cages tight to the ground. This way, heavy work boots won't be knocking them around!

The pruned clematis inside the cages will still get light and air. Their roots will be busy getting stronger and stronger to "attack" the new deck with a beautiful vengeance!

I know this system works. I used similar, but larger, "cages" to protect a couple huge hostas while we were getting a new roof and windows.