A picture would help. But no, I never cut off the leafless vines unless they are brown, dry, and clearly dead. Leafless vines will eventually produce leaves and often the peduncles for blooms. Pubicalyx is notorious for sending out leafless vines looking for something to twine onto. They will twine up onto just about anything, a trellis, a stick, even a string. Or they can be left to cascade.

Thank you for your help. I'll leave the vine intact. Would it be okay to bury the vine? All the roots are coming from it, I'm not sure if the roots would dry out if the vine isn't buried.

I think your instincts to bury are correct. It looks like it was buried already.