Jan make sure that you are covered and take a shower for your clothes in the washer when completed
Cut at the base and apply herbicide. Once withered, vines can be more easily removed. It can still infect you so wear protective attire.
Using a pitchfork, gently work some of the roots to the surface. Apply a herbicide for poison ivy to the plant and exposed roots. Reapply if necessary and watch the surrounding area for it to crop up. Once dead, gather your supplies: a big trashcan lined with a plastic bag, clippers, plyers, shovel, garden rake, alcohol, 2 extra pair of plastic gloves.
Cover yourself (even though all my clothing goes into the washing machine immediately afterward, I save my used disposable paint suits to use.) Use Armor pre-exposure lotion or Dawn dishwashing detergent on any exposed skin. Cover your shoes with plastic bags.
Wearing plastic gloves use the plyers to hold the vine or root. Clip and place in trashcan. Use the garden rake to break up the soil where the poison ivy has been. Anything the plant has touched, even dirt has urushiol on it. When done, remove plastic gloves, put in trash bag and put the other pair on. Clean all utensils used with alcohol. Don’t forget the handles. Lay safely aside. Plastic bag, paint suit etc. go into the plastic trash bag. Take your body to the washing machine where the lid is open. Remove clothing and wash in cool to medium water. Take a shower in the same temperature with Dawn.
Now babysit the area where it was for a couple of years for it to reemerge.
I got the heavy duty spray for trees and shrubs and used it liberally. As each time you get a reaction, the reaction is worse than the last, I was not going to tempt fate by doing anything but kill it from as far away as I could. The spray worked and my yard has been ivy free for over 10 years.
Poison ivy spray is the only sure fire way, you have to let it kill the vine and get down into the roots, so don't cut the vines, let them die back.