The Collaborative International Dictionary of English v.0.48:

Extermination \Ex*ter`mi*na"tion\, n. [Cf. F. extermination.]
   1. The act of exterminating; total destruction; eradication;
      excision; as, the extermination of inhabitants or tribes,
      of error or vice, or of weeds from a field.
      [1913 Webster]

   2. (Math.) Elimination. [R.]
      [1913 Webster]

WordNet (r) 3.0 (2006):

extermination
    n 1: complete annihilation; "they think a meteor cause the
         extinction of the dinosaurs" [syn: extinction,
         extermination]
    2: the act of exterminating [syn: extermination,
       liquidation]

Moby Thesaurus II by Grady Ward, 1.0:

54 Moby Thesaurus words for "extermination":
   abolishment, abolition, annihilation, annulment, bane, blood,
   bloodletting, bloodshed, braining, choking, choking off,
   dealing death, deracination, destruction, destruction of life,
   dispatch, elimination, eradication, euthanasia, execution,
   extinction, extinguishment, extirpation, flow of blood, gore,
   immolation, kill, killing, lapidation, liquidation, martyrdom,
   martyrization, mercy killing, negation, nullification, poisoning,
   purge, ritual killing, ritual murder, rooting out, sacrifice,
   shooting, silencing, slaughter, slaying, snuffing out, stifling,
   stoning, strangulation, suffocation, suppression, taking of life,
   uprooting, voiding