Apply a fluazifop-p-butyl postemergent herbicide to the top foliage of the white bird-of-paradise. Follow the package directions. The foliage will absorb the herbicide and transmit it to the roots.
Wait the time instructed on the package of herbicide for the chemicals to take effect. Once the time has passed, cut the bird-of-paradise back to the ground with a handsaw or pruning shears, depending on the size.
Dig out the root ball with a shovel. This will kill any remaining roots that the herbicide did not reach. Dig a circle around the plant that is 4 feet in diameter, then dig down under the root ball. Pull up the trunk and discard it.