Name: Michele Roth N.E. Indiana - Zone 5b, and F (Zone 9b) I'm always on my way out the door..
Butternuts are pretty big vines, aren't they? I'd say cut off at the soil line (don't pull) the weakest-looking one now, and then in a week or so, choose another to cut away...leaving just the healthiest one to grow on to maturity.
