To kill a standing tree, frilling and girdling are two practices you should understand. To girdle a poplar, cut a groove into the tree's trunk all the way around, penetrating at least 1/2 inch on small trees and 1 1/2 inches on full-grown trees. You need to cut through to the sticky layer, or cambium, under the bark. Use an ax, saw or chainsaw to make the cuts. Make a second cut 2 to 4 inches from the first so there are two complete circles around the tree. Frilling has the same effect. Use an ax to chop downward through the bark and cambium over and again in a full circle around the bark. This will peel down the bark and first layer of the trunk, creating a "frill" around the trunk.