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To cut something or some portion off of some larger thing or piece, with or as with a blade. A noun or pronoun can be used between "slice" and "off." Debris from the crash sliced his hand off. Slice off a piece for me, will you? We'll have to slice off any branches showing signs of rot.
slice something off
to cut something off with slicing motions. Sue sliced the dead branches off with a tree saw. Karen sliced off a nice piece of turkey.
To cut something from a larger piece: I picked up the knife and sliced off a piece of cheese. The chef held the pineapple down and sliced the top off.