How do you kill climbing ivy on a very old oak tree?

The tendrils and vines will need to be gently cut out of the tree and removed. You should not need to top the tree or remove branches. Also, cut the vines off at ground level and use a plant killer on the remaining roots. Be careful in selecting a type of killer that will not damage the tree. If the vine is extensive, it may be preferable to consult an arborist.