Oleander is a hearty shrub that requires a multiple step approach to eliminate, including cutting back the plant, treating the stump with herbicide, stump removal, continuing to monitor for growth and spraying any new growth with additional herbicide. Since the plant is toxic, anyone trying to remove it should wear proper protection.
SF Gate recommends using sharp pruning shears to cut back all growth, leaving only a stump. It recommends placing the stems in sturdy plastic garbage bags for removal. Burning of any part of the oleander plant is not advisable, as the smoke is an irritant and causes a severe reaction.
Stump removal involves creating cuts every one to three inches apart on the stump using a hatchet and spraying approximately one teaspoon of a glyphosate herbicide into each cut. The herbicide requires about one week to work and needs reapplication if rain falls within six hours of the initial application. After the week has passed, the homeowner digs the stump and root-ball from the ground manually and disposes it in plastic bags. He should remove as many of the plant debris as possible.
Roots left in the backfilled hole are likely to sprout, especially during the remainder of the growing season. Reapplication of glyphosate helps to eliminate the formation of new plants.