Now's the time to do it, yes, give it time to recover as the growing season goes on. Try to cut back to healthy buds though, because obviously, this one isn't meant to be cut back hard or pruned on a regular basis, but it should be fine.

Cut mine back almost flush to the ground in order to place a taller frame secured to deep seated rebars. Thinking that cutting it down so close killed it, I had intentions of planting a different clematis but it started coming back in several weeks and by the next year it had made it to the top of the new support and flowered with a vengeance. I never cut it back so close again but goes to show you that it is a tough vigorous plant.

Thank you both. I'm relieved to hear that I'm not likely to kill it but a little alarmed as to how I'm going to fix up anything large and strong enough for it. It used to grow over a wooden arbour but I moved that to a better position for sitting in. Now I've given myself another problem!

What I did was to take two trellises (in my case, decorative wire ones which are lighter than wood but still sturdy) and fastened one atop the other using electrical ties. For support I used 4 ft iron
rebars each driven two feet into the ground on ether side of the trellis and secured the trellis to the rebars with an ample number of electrical ties. I also placed a 5ft rebar in the middle of the width of the trellises for added verticle support. This arrangement has taken winds over 60 mph with no distortion for many years. Now, what are "rebars"? They are iron rods used in reinforcing concrete but have many uses in the garden. Many hardware stores have them in stock and come in various precut lengths or the store can make a custom cut for you. They can be driven into the ground (need some muscle in case you hit hard pack on the way down) by a mallet, wide head hammer or in my case when my neighbor had a new baby in the house, a nice quiet rubber mallet:)