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The expressions "make the grade" and "make the cut" mean the same according to all dictionaries.
But how can the two expressions mean the same ? "Grade" and "cut" do not mean the same thing.
While "make the grade" means "to reach a required level" , "make the cut" should mean "to be retrenched or laid off".
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To "make it" is to succeed. To "not make it" is to fail. (Sorry about the split infinitive, Jim. I don't know how else to say it.)
He did not make the cut.

"Not to make it" is to fail. (It doesn't have the same impact.)
Comments  
The way I understand this idiom, the "cut" is the sharp line that is drawn dividing the successful from the unsuccessful. If you "make the cut", you fall on the successful side of this line.
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