I cut the dead parts in sections of about 12" and just pull them off. If the tendrils don't come off I with the section I just pluck them off with my hands.

I clip where I want them pruned, a couple of buds up from the base, and then grab the bottom of the cut stems and pull. Most of the vines come off without problems, and any remaining crumble off when I run my hands over the trellis. This is one reason I prefer using metal or bamboo supports to having netting, since for me the vines haven't broken free of the netting as easily as from stiffer suppports.