The word is 'exterminate', which means 'to eliminate'. The reason I think this is a weird word is because the root word 'terminate' also means 'to eliminate'. For some reason adding the 'ex-' modifier doesn't change the word's meaning at all.
Usually adding the 'ex-' modifier makes it the opposite meaning. An 'ex-wife' is a former wife, an 'ex-convict' is a former convict, and an 'ex-basset hound' is what I would like to see happen around here three times.
But when you 'ex-terminate' something you don't actually bring it back to life. You kill it, just as if you 'terminate' it. This is annoying to me, but it's also useful to talk about dogs you want to get rid of - either word applies.