Blunt objections raised over qualification (7)

'blunt' is the definition.
(to stub is to blunt)

'objections raised over qualification' is the wordplay.
'objections' becomes 'buts' (I've seen this before).
'raised' says the letters should be written in reverse.
'over' is a charade indicator (letters next to each other).
'qualification' becomes 'bed' (abbreviation for Bachelor of Education degree).
'buts' written backwards gives 'stub'.
'stub'+'bed'='STUBBED'