Best to ID the vines first. I use inaturalist for quick suggestions of what a plant might be if I don’t recognize it, then compare close up pictures to what I’m seeing. This will let you know if you need any ppe for the task and can inform what you need to do afterwards to keep them from covering the tree again.

To your question - yes, cut the vines at their base. Some vines secure themselves very tightly to the tree, others have a looser hold. If these vines are wound very tightly to the tree it would be worth cutting them, then letting the upper growth die back before pulling it from the tree. Doing it this way can prevent damage to the bark and cambium of the trees you’re freeing.