Also, cut that. Stop, as in I won't stand for that—cut it! or If you don't cut that, I'll tell. [Slang; first half of 1800s] Also see cut it out.
Manage, tolerate, as in I don't know how he can cut it. [Slang; c. 1900]
Be effective, prove satisfactory, as in She's getting old and can no longer cut it. [Late 1900s] For a synonym see cut the mustard. Also see the subsequent entries beginning with cut it.