Select a product containing the chemical glyphosate for getting rid of the bois d'arc tree. Glyphosate is a general use, nonselective herbicide that kills all vegetation, including trees and grass. If possible, choose an undiluted, water-soluble formula, as these are more effective than oil-soluble formulas or esters.
Cut the tree down to a stump using a sharp axe. Make sure that the stump surface is level and smooth to ensure an even application of the chemical. Though glyphosate may be used at any time of the year, the recommended time is during August and September.
Apply the herbicide to the entire surface of the stump if the diameter is less than 3 inches. On stumps with a diameter of more than 3 inches, apply the chemical only on the 2 to 3 inches of the wood next to the bark, as the heartwood on larger trees is already dead. Avoid using glyphosate on very hot days or on stumps of severely drought stressed trees. Do not use if there is a chance of rain within six hours of chemical application.
Repeat application after seven to 10 days.
Leave the dead tree stump as it is or use a stump grinder to grind it to a depth of about a foot below the ground.