Chopping usually helps Clematis rather than hurts them. It should be just fine and may sprout additional vines up from the crown.

I had the same thing happen to me. My dad and I were doing yardwork this weekend, when he proudly proclaimed "I got that damn vine off the crabapple tree finally!"

I said, "oh the white clematis I planted in May that finally started to climb in the direction I want!" That's ok, maybe next year...arg.
He felt bad, but eventually I cooled off and reminded him to ask first, then cut.

I figure it had all summer to establish itself some, so maybe, just maybe it will come back out in the spring. For now, I am just treating it like it is still ok, watering well, mulch, etc. Mine was vining well too. I had just gotten it to vine up an obelisk trellis. It was about 3 to4 ft long!
Oh well, live and learn I guess! lol