Poem from minister shortly cut (8)
I believe the answer is:
clerihew
'poem' is the definition.
(clerihew is a kind of poem)
'minister shortly cut' is the wordplay.
I cannot quite understand how this works, but
'cut' could be 'hew' (I've seen this before) and 'hew' is located in the answer.
This explanation may well be incorrect...
'from' acts as a link.
Can you help me to learn more?
(Other definitions for clerihew that I've seen before include "Two-lined comic verse" , "Short comic rhyme" , "Short comic verse form" , "two couplets" , "Bentley's jingle" .)