Bush Honeysuckle is very difficult to get rid of. You can't just cut it down as it just grows back. You need to cut and use a strong herbacide like Glyphosate (which I DON'T like using) on the stump. In the fall it gets red berries that birds eat and then spreads in the droppings which spreads the plant like wildfire. I have been on a mission to eradicate it from my propery (10 acres) and have been at it a couple of years. Once cut and sprayed you will need to continue to monitor and spray once in the spring and once in the fall of any new plants or growth. The problem with this plant is it creates a canopy that keeps desirable hard wood like oaks, hickory, and maples from being able to grow. Good Luck!