Takes head off writer for making a point
I believe the answer is:
pencil sharpener
'takes head' is the definition.
The definition suggests a singular noun which matches the answer.
'off writer for making a point' is the wordplay.
I cannot quite understand how this works, but
'writer' could be 'pencil' (I've seen this before) and 'pencil' is located in the answer.
'a' is present in the answer.
'point' could be 'ene' (ENE is an example) and 'ene' is present in the answer.
This may be the basis of clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for pencil sharpener that I've seen before include "that makes lead go further" , "It's used to make a point" , "something struggling writer might resort to" , "Desk item" , "shaving device" .)