Have advantage over minion, one much applied to grindstone (4,4)
I believe the answer is:
edge tool
'one much applied to grindstone' is the definition.
(tool which might be sharpened with a grindstone)
'have advantage over minion' is the wordplay.
'have advantage over' becomes 'edge' (I can't justify this - if you can you should give a lot more credence to this answer).
'minion' becomes 'tool'.
'edge'+'tool'='EDGE TOOL'
(Other definitions for edge tool that I've seen before include "Chisel or knife, say" , "Maybe saw" , "Knife or axe, for example" , "Implement with one or more cutting sides" .)