Treatment providing cure - cut up an eccentric (11)
I believe the answer is:
acupuncture
'treatment' is the definition.
(acupuncture is a kind of treatment)
'cure cut up an eccentric' is the wordplay.
'eccentric' indicates anagramming the letters.
'cure'+'cut'+'up'+'an'='curecutupan'
'curecutupan' with letters rearranged gives 'ACUPUNCTURE'.
'providing' is the link.
(Other definitions for acupuncture that I've seen before include "Complementary medicine using needles" , "Method of treatment with needles" , "Alternative treatment using needles" , "Pain relief by needles" , "Form of alternative medicine" .)