With Zacsmaster on this. We generally cut through ivy stems where ivy may be hiding defects in the tree. We reinspect the tree 9 months to one year later once ivy has died off.
i have 3 trees in my garden all covered in ivy , last year i wanted to remove them to build a wall. Once i had removed the ivy the trees underneath were totally dead almost fell down on there own. It may vary species to species but the impression i get is that it sucks the life out whatever its growing around