What is the best method to cut this back in spring?

Hello. Normall I try to cut back late in automn but for an back in marmelade and spine problems I couldn't. I have a vine that was growing in an area along a wall when we moved here. I replanted this vine (don't know the name) makes loads of cream small flowers like grapes towards end of summer. The vines grow VERY fast. I have been winding and building it up to get a nice sort of arch that creates privacy from neighbors. but over the years it center becomes more and more heavy that I had to add some sort of help to hold it up as it starts tilting.
QUESTION:
How much can I cut back and still get new growth to keep the privacy? I just trimmed it now some branches have turned hard like wood but in the center many are very thin brittle that just fall down when pushed a bit.
Cleaning out EVERYTHING apart from the hardened branches worries me as the new grows seem to start at all the thin ends. I don't want to end up with a naked structure for summer. Its very difficult to follow each vine to its beginning.
Its more easy to simply cut a general topiary shape. Thanks for any advice this needs to be done soon as in now as it is starting to sprout.