One method of killing a palm tree is to drill several holes into its trunk and fill them with herbicide. Killing the tree may require several applications of herbicide.
Drill three holes into the trunk of the palm tree at a slight downward angle. The holes should be approximately a half-inch in diameter and should reach the center of the tree. Fill the holes with an herbicidal solution of glyphosate. Allow the holes to drain. Large trees may require several applications of herbicide. If the tree does not show signs of dessication, such as brown leaves and drying, within three weeks, the process may be repeated as necessary until the tree is dead.