Cutting tool incorporated is worn in the middle? (7)

I believe the answer is:

incisor

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'cutting tool' is the definition.
The answer and definition can be both body parts as well as being singular nouns.
Maybe there's an association between them I don't understand?

'incorporated is worn in the middle?' is the wordplay.
'incorporated' becomes 'inc'.
'in the middle?' indicates the central letters (I've seen 'in the middle' mean this).
The middle of 'worn' is 'or'.
'inc'+'is'+'or'='INCISOR'

Can you help me to learn more?

(Other definitions for incisor that I've seen before include "Ivory perhaps" , "carnivore requires?" , "Front tooth" , "companion could be Goofy" , "something with bite" .)

I've seen this clue in The Irish Times.

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