Pour rock salt around the tree at its base. Bear in mind that the rock salt will damage any existing plant life in that area and harm the soil. Apply ½ cup of rock salt for smaller trees, and up to several cups to fully cover the base area of larger trees.
Use a chainsaw, hand saw or axe to slice a vertical cut in the trunk of the tree as close to the ground as possible. Wait at least a week. Fungus should hopefully enter the sliced area of the stump and infect the tree, helping to kill it.
Use the axe, hand saw or chainsaw to cut the tree down. Use an electric drill to drill a series of holes into the top of the trunk. Drill the holes a few inches apart around the perimeter of the trunk's surface, so that you form a circle of holes.
Purchase a stump killer solution, available at most home service centers. Pour the solution into the holes previously drilled into the trunk. Saturate the entire trunk with the solution as well.
Use a garden hose to saturate the trunk and surrounding area with water. Continue to over-water the area to promote root rot. Use twice the amount of fertilizer recommended by the fertilizer manufacturer. Over-fertilizing the area will also help kill the evergreen's root system.