Cuts out a piece of nickel I destroyed (6)

I believe the answer is:

elides

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'cuts' is the definition.
Although both the answer and definition are verbs in their -s form, I don't see how one could define the other.

'a piece of nickel i destroyed' is the wordplay.
'a piece of' indicates a hidden word.
'ELIDES' is hidden within 'nickel i destroyed'.

'out' is the link.

Can you help me to learn more?

(Another definition for elides that I've seen is " Omits".)

I've seen this clue in the Sydney Morning Herald.

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