Looks like Trachelospermum. It gets all its nourishment from the ground so if you cut through all stems it will die. Then you'll probably need to pull the dead vines down. Unless the weather brings them down. Trachelospermum climbs by twining its stems so there will be no suckers attached to the pole.

Thanks for the reply floral_uk!

I forgot to mention that you will also need to kill the roots or it will start back up the pole.

What zone are you in?

Obviously somewhere warm enough for Trachelospermum to grow to that height. And for the Albizia in the foreground and the Oleander in the background to thrive.