Move your potted Philodendron outdoors in fall and place it in an uncovered area where frost or snow is likely to occur.
Water your plant every day, whether it is indoors or outside, keeping the soil wet. If your Philodendron sits on a plant saucer, keep water in the saucer at all times. In time, the roots will rot, the leaves will turn yellow and the plant will die.
Remove your Philodendron from its pot and put it in an area where the sun will bake the plant, such as a paved driveway. Cover it with a sheet of heavy-duty clear plastic to speed the process.
Deprive your Philodendron of light. Move it into a closet or other dark area: if you have a garage that also gets cold, that would be a good place to locate a plant you want to kill.
Cut large Philodendrons that climb trees at the soil line and then drill holes into the stump. Treat with an approved herbicide by shooting the product into the holes.