Wearing safety goggles and gloves, cut the shrub down to ground level with a chain saw. Roll or drag the shrub to the street corner for regular trash pickup.
Excavate a few inches into the ground around the shrub roots with a shovel.
Spray herbicide liberally onto the trunk and any exposed roots. Soak the trunk and exposed roots as much as possible.
Cover the shrub roots with a tarp to deprive them of sunlight and rainwater. Place bricks on the tarp to keep the wind from blowing it away.
Remove the tarp weekly and spray the trunk and exposed roots with herbicide, then re-cover. Repeat this for four to six weeks, until the shrub roots are dead.
Dig up the dead shrub roots with a shovel and dispose in the curbside pickup.