cut, whittle
刋 centers on cutting or shaving material away: to cut, whittle, or carve by removing thin layers.
刋 is a rare character. It combines 刂 (knife) with 千, which may have contributed the sound, but the exact historical development is uncertain.
A knife 刂 beside a thousand 千 thin shavings: imagine whittling a piece of wood, cutting away a thousand tiny curls.
For カン, picture a can being cut open with a knife: can -> カン, and the knife 刂 slices through the metal.