Cutting down a eucalyptus tree requires killing the stump so it doesn't sprout again. SF Gate recommends the use of drilling and the application of an herbicide before cutting to prevent regrowth.
Preparation includes using a 5/16-inch flat spade bit and electric drill. The process requires drilling the holes approximately 3 inches apart around the perimeter of the tree. Each should be a minimum of 2 inches in depth, ensuring the herbicide reaches the inner tree tissue. If preparing to cut down the tree during the dormant season, one should space the holes with about 1 inch in diameter as the transportation rate in the tree is slower and requires more of the herbicide to eliminate the tree.
In addition to the herbicide treatment, SF Gate recommends girdling the tree by cutting two 1-inch rings around the circumference with a chainsaw, and then removing the bark between the two circles, using a hatchet. Spraying again with herbicide is another option if one does not want to work at removing the bark.
After several weeks the tree is dead and ready to cut. At this point, the trunk and branches are ready for disposal in any method one wants as they are unable to sprout again. Removal of the non-native eucalyptus trees from locations in the United States helps to preserve the natural biodiversity from these invasive plants.