You can kill a honeysuckle plant by pulling it out yourself, cutting them, or in dire cases of invasions, by using herbicides. The first suggestion works only for young plants as most honeysuckle varieties have shallow root systems. Cutting them may not work if you're not diligent at it because it may just grow back days after being severed while using herbicides has its disadvantages as well.
Authorities on dealing with honeysuckles discourage cutting down the plants because new shoots will just sprout from the roots easily. However, some still cut the vines every now and then mainly to withhold the roots from getting the necessary nutrients. Another worthy suggestion involves bagging the severed tree to prevent it from being exposed to the sun.
If you want a more decisive action against honeysuckle invasion, use an herbicide solution containing one percent glysophate. Depending on the area of infestation, you can increase the solution level to up to a 30 percent solution of glyphosate. However, using herbicides can potentially kill surrounding plants as well.
The honeysuckle plant was originally planted in the United States during the 50's and 70's because of its ornamental value. It is also supposed to help control soil erosion and provide shelter and food for wildlife. While its flowers are brilliant and lovely, its aggressive reproductive ways pose problems for the native plants. What's more, its fruits have practically no nutritional value and its dense bushes prevent anything from living under it.