Removing Small Buckthorn Plants
Pour water on the soil surrounding small buckthorn plants that are smaller than 2 inches in diameter. Wet soil is more loose than dry soil and will make it easier for you to pull the the plants out.
Pull the plants out with your hands if it is no larger than 3/8 inch tall. The root systems of buckthorns this size will be very small and easily removed from the soil.
Use a weed wrench to remove buckthorns larger than 3/8 inch tall. A weed wrench is a hand device that will dig to the bottom of the root system and remove the entire plant. Using a tool for a buckthorn this size is necessary to ensure the entire root system is removed. (Anything left over may sprout into another full-grown plant.)
Removing Large Buckthorn Plants
Cut the buckthorn at the base with a saw if it is more than 2 inches in diameter.
Spray the top of the stump with professional-strength herbicide until the stump is completely covered. You can find professional-strength herbicides at most home improvement stores. Make sure you only spray the stump and not the surrounding soil, since most herbicides are non-selective and will kill most vegetation they come in contact with. Do not stand directly over the stump when spraying the herbicide, in order to avoid breathing in the fumes.
Cover the stump with dark-colored plastic (such as a black trash bag or a plastic tarp) to prevent sunlight from shining on the plant.
Return to the stump after one week to see if any new branches are sprouting. If so, spray with more herbicide and cover again. It may take two to three applications of herbicide to completely kill the buckthorn since it is an extremely hearty plant. This translates into a 2-to-3-week project.