Cut at the base and apply herbicide to the base. Remove once they are withered, it's easier and the little grippers wither as well. Dress with caution because even dead they can produce a rash.
Charles, this recipe will kill any plant like vines, weeds etc and is not harmful to pets and people etc. I would use a long handle to spray it so you do not get in it yourself. Hope this helps. The tutorial is on saving weed eating, but it is good for ANY unwanted plants, esp. the poison types!
Round-Up.......cut if off,wearing mask & gloves and long sleeved pants shirts remove tops put in garbage bags( thoroughly wash clothing shoes tools anything that you have used to remove the tops;get 2 gallon pump sprayer(not a back pack don't risk leaking solution on your back) buy concentrate Round-Up add food coloring to it(so you can see where you are spraying it) as soon as you see new leaves growing on stems spray them heavily with the Round-Up. It is absorbed into leaves them stems then kills root systems. Round-Up works best when plant is in vigorous growth after being cut off & new leaves are emerging.Keep checking for new growth and spray thru out growing season.Depending how big the area is it may take a few weeks to get it all. Put spray nozzle down onto leaves when spraying & do not spray in wind or breezy conditions;use gloves;do not walk or get in wet solution. Follow the safety instructions on container they are & have always been on the container for a reason. If the vines are up on trees they need cut off and let them die then pulled off trees. They will release easier if /when dead. Spray any new growth coming from cut off vines as soon as it has a few leaves to absorb the round up. If the vines are old big/thick bigger than 1/2" mix the round-up 1/2 concentrate and 1/2 water need it strong.stay on top of new growth look for sprouts all over area and the following Spring.try to keep area raked so you can see any new growth starting anywhere.
I would definitely recommend using a poison oak spray, they make one specifically for poison ivy and oak and it kills it down to the root. Don't remove any of the plant, let it die down on it's own so the roots don't spread or come back.