This is the sort of nonsense up with which I will not put (attributed to Churchill). There is nothing inherently wrong with the grammar when a sentence ends in a preposition. In this example, it seems 'over with' is a synonym for phrases like 'done and dusted', 'out of the way', and to me a slightly rhetorical form of 'finished' or 'completed'.
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Debpriya De"Let's get the job over" conveys the same meaning.No. This sounds incomplete. "over with" is the whole expression. It means "finished", "done".