Low state of mind daughter cast off (3)
I believe the answer is:
moo
'low' is the definition.
(both can mean to make a cow noise)
'state of mind daughter cast off' is the wordplay.
'state of mind' becomes 'mood' (one's mood is one's state of mind).
'daughter' becomes 'd' (genealogical abbreviation).
'cast off' indicates named letters should be taken away.
'mood' with 'd' taken away is 'MOO'.
(Other definitions for moo that I've seen before include "Guernsey noise?" , "Low (of cattle)" , "Cow's call" , "Cow's low" , "Cartoon sound of a cow" .)