Frenzied female, awfully mean, with a daughter (6)
I believe the answer is:
maenad
'frenzied female' is the definition.
(I've seen this before)
'awfully mean with a daughter' is the wordplay.
'awfully' is an anagram indicator.
'with' is a charade indicator (letters next to each other).
'daughter' becomes 'd' (genealogical abbreviation).
'mean' anagrammed gives 'maen'.
'maen'+'a'+'d'='MAENAD'
(Other definitions for maenad that I've seen before include "Female fan of Bacchus" , "Wild woman follower of Dionysus" , "Da, name the female follower of Bacchus." , "Frenzied or distraught woman" , "Name da for a fierce woman" .)