Eradicate
Part of speech: verb
Definition: To pull up by the roots; to uproot. To completely destroy; to put an end to; to extirpate.
Example sentence: In 1967, the world health community launched a global effort to eradicate smallpox. It took a coordinated, worldwide effort, required the commitment of every government, and cost $130 million dollars. By 1977, smallpox had disappeared.
Exterminate
Part of speech: verb
Definition: To kill all of a population, usually deliberate and especially applied to pests.To bring a definite end to, finish completely. A rather strong word that implies that what has been ended won't resurface.