Thanks for writing! Dutchman's pipe vines don't require any special pruning techniques --- so you can cut out whichever branches you need.
In general, most gardeners like to prune out the weakest, most scraggly growth, as well as any wayward shoots.
You can prune it back fairly hard --- just don't remove any more than 1/4 of the plant in one season.
As to when -- the best times are late winter/early spring or midsummer.
Good luck. I hope this helps!
---Justin, Senior Garden Editor, BHG.com