I did exactly that with a rose last autumn. It had been wonderful - bush rose - white - often had over a hundred blooms open at the same time, but it had got very scruffy and had lots of dead bits - so I thought - "it's kill or cure" and cut it right down from about 5ft to about 20" leaving one main trunk. It has produced a few small shoots, but I fear it will never return to its former glory. Alas, it is now for the Great Garden In The Sky.
I also have a climbing rose which refuses to shoot where I want it to, in spite of careful pruning. Lots of bits have died, lots of sideshoots have sprouted too low or too high. Even though I bought it from a very expensive rose-grower, having read all the promises about its growth-habits, which were rubbish. That rose, too, is for the GGITS very soon.