I am extremely allergic to poison ivy. We purchased land and built a house on the land commencing in 1989. There was lots of poison ivy on the property, including a vine the size of a man's forearm hanging in an old hackberry. My wife and kids, who were not bothered, pulled or cut down poison ivy, including the arm sized vine. We dumped the material in a ditch and later covered it with dirt. I have cut down and cut up and burned many trees that had poison ivy in them without getting a case. As long as the vines are completely removed from the tree you will be fine. If, however, you cut into a vine that is still attached to the tree, you can get poison ivy from that.