Crookedly makes cuts, unedifyingly including education (10)
I believe the answer is:
Here is my best explanation:
'crookedly' is the definition.
'cuts unedifyingly including education' is the wordplay.
'cuts' becomes 'lops' (lopping is a kind of cutting).
'unedifyingly' becomes 'idly' (I can't justify this - if you can you should believe this answer much more).
'including' is an insertion indicator.
'education' becomes 'ed' (abbreviation - e.g. sex ed).
'idly' placed around 'ed' is 'idedly'.
'makes' acts as a link.