If your vine has tiny red flowers and feathery foliage, it re-seeds itself. It is very difficult to kill off.Mine has spread from my front yard to my back yard. Even just pulling up the dead plant will spread the seeds! Good luck!
There are so many vines that are called "hummingbird vine". It is difficult to advise you without knowing which vine you actually have. If it is the one with the feathery leaves you can cut it back any time now in your zone since it reproduces from seed. But if it is the hummingbird vine that has the huge trumpet flowers then wait until frost is over to cut it back since it is perennial. Can you look it up in a book or online to find out which one you have?
Do you mean a trumpet vine? If so, it will grow from the already established vines, you can just prune it to shape. This is a vigorous grower that will be hard to keep up with once fully established. It will start new plants from its roots that will pop up all over your yard if pruned too aggressively. It is near impossible to kill if you want to get rid of it. I've cut back, dug up, used round-up (which I really don't like), continually on mine for 3 years, and am still fighting mine. Don't worry about harming this plant, it is very hardy.
If you mean honeysuckle, you can again cut it back at any time--it is extremely hardy too. I've cut mine back and dug some of the roots and it still grows (but it was very well established).
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