Family left, mistaking poor mark (6)
I believe the answer is:
stigma
'mark' is the definition.
('stigma' can be a synonym of 'mark')
'family left mistaking poor' is the wordplay.
'family' becomes 'kin' ('kin' can be a synonym of 'family').
'left' indicates named letters should be taken away.
'poor' indicates an anagram.
'mistaking' with 'kin' removed is 'mistag'.
'mistag' anagrammed gives 'STIGMA'.
(Other definitions for stigma that I've seen before include "Bad mark" , "Mark of dishonour" , "Badge of shame" , "part of plant" , "Part of a flower" .)