To meet or come up to a required standard (from golf where a player must do equal or better than a certain score to continue)
e.g. 1 (original meaning)
The young player did not make the cut and was unable to join the team that year.

e.g. 2
Some say if Pluto were discovered today instead of 75 years ago, it woundn't make the cut.
(From this article about the potential 10th planet of the solar system (9 is the current recognized number), Pluto, the 9th and currently outmost planet was discredited by the newly discovered planet further away from the Sun)
by llong August 13, 2006
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Idiom

to be finally selected
For every music album, song-writer writes many more songs out of which 12 or 15 are selected for the release, the rest that don't make the final cut are released in the Deluxe version of the album later on.
by Zami Karzai September 22, 2018
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