The verb extirpate originally meant "to weed out by the roots." Now you can use it more broadly to describe getting rid of something completely.
Use the verb extirpate when you mean to destroy completely or get rid of completely. If you came home from vacation with your luggage infested by bedbugs, you will need to call an exterminator to extirpate them. The dodo bird was extirpated due to hunting and the introduction of predators in their habitat.