1. cut it fine - Verb
2. cut it fine - Phrase
(idiomatic, UK) To achieve something at the last possible moment, or with no margin for error.
(idiomatic, UK) To be stingy.
1908 October, Kenneth Grahame, The Wind in the Willows, New York, N.Y.: Charles Scribner’s Sons, →OCLC:“O stop, stop,” cried the Mole in ecstacies: “This is too much!”“Do you really think so?” enquired the Rat seriously. “It’s only what I always take on these little excursions; and the other animals are always telling me that I’m a mean beast and cut it very fine!”
Used other than figuratively or idiomatically: see cut, it, fine.
Source: en.wiktionary.org