How do I kill or cut back ivy without injuring tree?

Over the years I’ve allowed English ivy to grow up a stout sycamore tree. But by now it has nearly enveloped the trunk and reached 60′-70′ high, spreading out on the branches. It hasn’t seemed to be a problem except when heavy snow and/or ice adds its weight to the ivy. My question: How do I kill or cut back the ivy without injuring the tree? I don’t want to lose the mature tree.