【Exterminate】 , 【extirpate】 ,  【eradicate】 ,  【uproot】 ,  【deracinate】 ,  【wipe】  are comparable when they mean to effect the destruction or abolition of something.

【Exterminate】 implies utter extinction; it therefore usually implies a killing off.

【Extirpate】  implies extinction of a group, kind, or growth, but it may carry less an implication of killing off, as  【exterminate】  carries, than one of the destruction or removal of the things essential to survival and reproduction; thus, wolves might be exterminated by hunting in a particular area, but large carnivores in general are extirpated by changed conditions in thickly settled regions; a heresy is often extirpated, rather than exterminated, by the removal of the leaders from a position of influence; a vice cannot easily be extirpated so long as the conditions which promote it remain in existence.

【Eradicate】 stresses the driving out or elimination of something that has taken root or has established itself.

【Uproot】  differs from  【eradicate】 chiefly in being more definitely figurative and in suggesting forcible and violent methods similar to those of a tempest that tears trees out by their roots.

【Deracinate】  basically is very close to  【uproot】 , but in much recent use it denotes specifically to separate (as oneself or one's work) from a natural or traditional racial, social, or intellectual group.

【Wipe】  (in this sense used with out ) often implies extermination, but it equally often suggests a canceling or obliterating (as by payment, retaliation, or exhaustion of supply).