Crossword Genius

Abandon a kiss with workmate, ultimately (3)

Ross

I believe the answer is:

axe

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'abandon' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.

'a kiss with workmate ultimately' is the wordplay.
'kiss' becomes 'x' (X can represent a kiss).
'with' says to put letters next to each other.
'ultimately' indicates one should take the final letters.
The final letter of 'workmate' is 'e'.
'a'+'x'+'e'='AXE'

Can you help me to learn more?

(Other definitions for axe that I've seen before include "Chop" , "Eliminate" , "Means of cutting" , "Dispense with" , "US jazz instrument" .)

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