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The stray, after the “Scat!” scampers off (8)

Ross

I believe the answer is:

castaway

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

'after the scat scampers off' is the wordplay.
'after' is a charade indicator (letters next to each other).
'the scat scampers' becomes 'cast' (I can't justify this - if you can you should believe this answer much more).
'off' becomes 'away' ('away' can be a synonym of 'off').
'cast' next to 'away' is 'CASTAWAY'.

Can you help me to learn more?

(Other definitions for castaway that I've seen before include ""Captain Bligh"? - with 5d" , "Stranded person" , "Robinson Crusoe was one" , "Type of lace" , "Shipwreck survivor" .)

I've seen this clue in the Evening Standard.
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