Demolish middies, ship out (9)
I believe the answer is:
dismissed
'out' is the definition.
'demolish middies ship' is the wordplay.
I cannot quite see how this works, but
'ship' could be 'ss' (prefix in ship names eg SS Great Britain) and 'ss' is found within the answer.
an anagram of 'middies' is 'dismied' which is located in the left over letters.
No letters remain.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for dismissed that I've seen before include "Brushed off or sacked" , "put out of court" , "Fired" , "Spurned" .)