Spay one's mutt here in the centre (6)

I believe the answer is:

neuter

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'spay' is the definition.
(synonyms)

I don't understand the remainder of the clue.

(Other definitions for neuter that I've seen before include "Of noun, neither masculine nor feminine" , "Retune (anag.)" , "Sexless" , "Neither masculine nor feminine gender" , "Castrate" .)

I've seen this clue in The Irish Times.

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