School mom dumps married idiot in New York (5)

I believe the answer is:

schmo

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'dumps married idiot in new york' is the definition.
I can't judge whether this definition defines the answer.

'school mom' is the wordplay.
'school' becomes 'sch' (common abbreviation).
'mom' becomes 'mo' (I am not sure about this - if you are sure you should believe this answer much more).
'sch'+'mo'='SCHMO'

Can you help me to learn more?

(Other definitions for schmo that I've seen before include "jerk" , "Inept person (US_informal)" , "Boring American" , "clot" , "Fool (Yiddish)" .)

I've seen this clue in The Guardian.

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