The butterfly bush, also known as the summer lilac or orange eye, originated in China and provides sustainable nectar to adult butterflies. Requiring almost no upkeep, it is virtually indestructible. The qualities that make it easy to cultivate also allow it to become invasive in the landscape. It crowds out other plants and provides an inhospitable environment to native insects and animals. Because of this, you may want to remove a butterfly bush. They can be quite hard to kill and often will re-sprout from their roots if you cut them to the ground. In order to eradicate it, you will need to kill the roots of a butterfly bush.
Use a pruning saw or shears and cut the butterfly bush down to the ground. Leave a few inches of stump above the ground for a means of applying herbicide.
Apply a non-selective herbicide like Roundup to the remaining stump. Non-selective herbicide will kill any plant it comes in contact with. The stump will absorb the herbicide and transport it to the roots, where it will achieve a total kill.
Watch for shoots around the stump. If any appear, immediately treat them with herbicide.
Dispose of all branches by taking them to a landfill, putting them in your yard waste container, or by burning them.