Unlikely that you have killed it but you have pruned too early and removed all the flower buds.

Spring flowering Clematis flower on growth produced the previous year if you need to prune do so lightly to remove spent flowers immediately after flowering.

Old, woody plants can be pruned very hard - down to a couple of feet if necessary, after flowering to remove lots of the old, non-flowering growth. They may take a year or so to fully recover and start flowering properly again, they may also not recover.

I think you've cut off all the buds. Chances are with the harsh winter it's been a bit later to bud and now you've cut them off :(, just leave it for now and see if it recovers .....

You should complain if it was a new plant - the instructions are utterly wrong. That's such a pity for you to lose this year's flowers.

The info on most Clematis plants says to cut down to about 30 cms immediately after planting. This is to encourage new stems so you get a better plant eventually. After that you need to prune different ones differently. Was this a new C. montana or an established one?

I'd imagine the label simply said prune in Spring, rather than in spring immediately after flowering. Its not spring yet anyway, it's still winter, and will be till mid March, so sorry Julier, you got it wrong - leave it alone this season and it should flower next year - and if you want to prune it after its finished flowering, then do.