Getting rid of silly mini tagline (11)
I believe the answer is:
eliminating
'getting rid of' is the definition.
('eliminate' can be a synonym of 'get rid of')
'silly mini tagline' is the wordplay.
'silly' is an anagram indicator.
'mini'+'tagline'='minitagline'
'minitagline' with letters rearranged gives 'ELIMINATING'.
(Other definitions for eliminating that I've seen before include "Completely removing" , "Removing from contention" , "Getting rid of (something)" .)