Told to lift a cutter (5)

I believe the answer is:

razor

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'a cutter' is the definition.
(I know that razor is a type of knife)

I can't explain the rest of the clue.

(Other definitions for razor that I've seen before include "Shaving instrument" , "Shaving blade" , "Sharp implement" , "cut-throat" , "Implement for removing hair" .)

I've seen this clue in The Guardian.

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