Boston ivy (Parthenocissus tricuspidata) is similar to ivy, but is not actually part of the Hedera--or ivy--family. Like ivy, though, it is a climbing plant that affixes to solid surfaces. It sometimes causes serious damage to walls and other surfaces. So before you start tearing it away--which you shouldn't do anyway--know that you might cause further damage, or the damage may already be done; therefore, you may want to reconsider killing the Boston ivy and instead prune it back.
Cut down all the ivy with a pair of handheld clippers. Cut off all the foliage, but leave about an inch of stem, if possible. If the ivy is growing on a brick or concrete wall, do not pull. It may rip off some of the mortar, concrete or brick so clip it away close to the suckers. Check a small area for any damage already done by the Boston ivy to be sure you still want to remove it.
Spray an herbicide on the remaining stems. A product that contains glyphosate works well with Boston ivy. Be cautious and make sure you don't spray it on any other nearby plants.
Cut down any new growth immediately. If new growth somehow does occur after cutting back the plant and applying an herbicide, you must starve out the roots by preventing it from photosynthesizing sun into usable energy. Continue to cut the Boston ivy back until it no longer grows.