Put on a pair of protective gloves and a long-sleeved shirt before beginning.
Trim the oleander shrub's branches back as close to the ground as possible with a pruning saw.
Monitor the oleander stump closely for signs of new growth, which will likely take one to three weeks to appear.
Fill a plant sprayer with 1 gallon of glyphosate herbicide, 1 tbsp. of liquid dishwashing detergent and 2 tbsp. of fine granular plant fertilizer.
Put on protective gloves and clothing before applying the herbicide.
Spray the newly developed oleander growth until it is dripping wet. Make the application when little chance of rain is predicted for the following two to three days. Take care not to spray surrounding plants because they may also be damaged by the herbicide.
Water the stump thoroughly after the foliage has turned completely brown, which works to stimulate new growth if any part of the shrub survived the first herbicide application.
Continue to monitor the stump for signs of new foliage. Repeat the application of glyphosate if new growth occurs.
Dig around the stump with a sharp spade until it is loose enough to be lifted from the soil after new growth stops and the stump begins to decompose.