Refers to actually removing hair with a razor or similar tool, often used literally. Tom had to shave off his beard for the new job.
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Physical Closeness
Emphasizes the closeness of the cutting to the surface, usually leaving very little behind. The carpenter had to shave off a millimeter from the door edge.
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Facial Hair Focus
Commonly used in reference to facial hair — beards, mustaches. She preferred him with a clean-shaven face, so he shaved off his stubble.