Hi Marla, try this, it should work...
Hi Marla: Get a product called ground clear, it kills everything! Then, put some in a small can and paint the undersides of the leaves with this, using a small foam brush. Be sure not to get the ground clear on anything else. The plant will take the poison to the roots, through the leaves, and kill just this plant - if you are careful not to get the ground clear on anything else. You can use this method on any plant you want to get rid of. If you are worried about the leaves touching your other plants, cut the unwanted plant short, leaving several leaves, paint the leaves with the ground clear and then cover it with a plastic bag and secure it to the ground. That way, even the wind won't blow the poisoned vine onto your other plants. Good luck with this, invasive plants are the worst!
If you are, or you know someone who is, diabetic, ask for one of their used needles, fill it with the ground clear and inject it, in a downwards direction, directly into the vine. Then, be sure to dispose of the needle properly and don't touch the needle part because you may get some of the stinging nettle oil on you. Good luck
You could try a weed killer, or pull them up by the root (wearing gloves)
DO NOT use the Ground Clear, or other poisons, they kill honey bees and other beneficial butterflies and insects that are around any of the plants. Put on leather gloves and pull it out, it’s much safer than using poisons and faster also.
Yup, that's right. You can eat stinging nettles and they are quite nutritious and I'm told, since I don't have them at present, tasty. So, don't let them go to seed but eat them and be healthier from it and it will extinguish them without harming the earth, but with helping you two-fold. Blessings!