Holly is a very hardy type of tree that is frequently associated with the Christmas holiday. Holly trees are generally difficult to kill and they can frequently grow back even after the tree has been cut down if steps aren't taken to kill off the root system in the soil. If a holly tree gets an infection or is interfering with the growth of other plants in your yard, it likely needs to be killed. Killing a holly tree does require some diligence.
Cut the tree down with a chainsaw or axe. You may need to use a professional service to do this to avoid the tree from damaging anything as it falls down and a professional service can also get rid of the tree for you.
Drill a 1.2 cm (1/2 inch) hole into the tree stump and add another hole every 15 cm (6 inches) around the stump's perimeter. Pack each hole with nitrogen fertiliser and water the stump regularly. This causes fungus to grow that will soften the stump over a period of four to six weeks. Drench the area around the stump with water during this time as well to drown the root system.
Dig the stump out of the ground with a shovel after it has started decomposing or you can use a stump puller. Once the stump is removed and the roots are severed, the holly tree should not be able to grow back.