1. Cut off the upper part of your old T-shirt.
2. Cut out the upper part of your old T-shirt.
3. Make a cut of the upper part of your old T-shirt.
4. Make cuts of the upper part of your old T-shirt.
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Are they all grammatical? Which expression should we use?
1 is correct. 2 is sort of correct, but doesn't mean the same thing as 1.
I'm not sure what you want 3 and 4 to mean, but the phrasing should be "make a cut in the upper ... " or "make cuts in the upper ... "