Margin, already mentioned in a comment, is relevant. From en.wiktionary, one of its senses is “A permissible difference; allowing some freedom to move within limits”, and another sense, less relevant, is “The edge defining inclusion in or exclusion from of a set or group”.
It may be preceded by error, as in error margin, slop, slack, or allowance.
In practice, you might hear “The rough cut's dimensions are the final cut's dimensions plus a skosh”. Skosh (“A tiny amount; a little bit; tad; smidgen; jot”) is one of many synonyms that Wikisaurus lists for terms related to the sense an amount of small or insignificant quantity.
Edit: Regarding Niall's question, “Wouldn't "Margin for error" be the common phrase?”, I agree that might be the case but cannot say for sure. Google ngrams for error margin,margin of error,margin for error is interesting but not helpful without further research, and the sentences “The rough cut leaves a 2 mm error margin” and “The rough cut leaves a 2 mm margin for error” have similar but different meanings. I'd not use either sentence myself, but would instead speak of tolerance (“The variation or deviation from a standard, especially the maximum permitted variation in an engineering measurement” — en.wiktionary), as in “The tolerance for the rough cut is +2/-0 mm”, meaning that the rough cut is allowed to be as much as 2 mm farther than its target, and is not allowed to be below its target length.