Protect your skin when you handle oleander plants. Wear gloves when you prune them, as the entire plant is poisonous and sometimes causes skin rashes. Also, stinging caterpillars sometimes use the oleander as a host plant.
Remove the large branches from older, established oleander plants. Saw or cut through large branches with loppers or a bow saw or pruning saw. Cut the branches as close to the main trunk as possible.
Saw the main trunk into sections, starting at the top of the plant and working toward the bottom. Cut the oleander stump as close to soil level as possible. Brush away any sawdust from the remaining stump. Sawdust will absorb the herbicide and keep it from entering the root system.
Use an herbicide containing triclopyr amine or glyphosate. Diluting the chemical concentrate prior to application is unnecessary, according to the University of Florida IFAS Extension. Shake the herbicide bottle to mix the ingredients, and apply it to the stump immediately after you cut down the oleander.
Pour a small amount of herbicide into a disposable plastic container. Dip a paintbrush into the herbicide concentrate, and saturate the cut section of the oleander stump. Coat the entire cut section with herbicide. Reapply the herbicide to the stump if new growth appears.