Destroy by degrees (5)
I believe the answer is:
erode
'destroy by degrees' is the definition.
(I've seen this in another clue)
This is all the clue.
(Other definitions for erode that I've seen before include "'Deteriorate, wear away (5)'" , "Become ground down or deteriorate" , "Grind down" , "fragment" , "Gradually destroy" .)