Baffle a half stupid politician (5)
I believe the answer is:
stump
'baffle' is the definition.
(thesaurus)
'a half stupid politician' is the wordplay.
'a half' indicates taking half.
'politician' becomes 'mp'.
'stupid' with half the letters taken is 'stu'.
'stu'+'mp'='STUMP'
(Other definitions for stump that I've seen before include "Flummox" , "Small remaining part; cricket item" , "Part of a felled tree that's left in the ground" , "Residue after felling" , "What's left after cutting" .)