Don't kill the neighbors tree. Prune the part hanging over your yard if you must. Place the material on his driveway, after all, it's his tree. The neighbor may take your need seriously after that.
You could also find something your neighbor wants and make him a deal he can't refuse.
11th commandment, Thou shall not kill thy neighbors ox, or his goats, or his trees, especially of the coconut, or his dog, or his cat, or his mango, or his avocado, or anything he keeps that bears tropical fruits.
You can replace kill with smite