Lacking a roof, hospital department cuts operations? (4-3)

I believe the answer is:
open-top
'lacking a' is the definition.
I don't know anything about this answer so I cannot tell whether it can be defined by this definition.
'roof hospital department cuts operations?' is the wordplay.
'roof' becomes 'op' (I can't explain this - if you can you should give a lot more credence to this answer).
'hospital department' becomes 'ENT' (Ear, Nose and Throat department).
'cuts' means to remove the last letter (I've seen 'cut' mean this).
'operations?' becomes 'ops' (abbreviation).
'ops' with its final letter taken away is 'op'.
'op'+'ent'+'op'='OPEN-TOP'
Can you help me to learn more?
(Other definitions for open-top that I've seen before include "Lacking cover" , "(Of car) not having a permanent roof" , "Like some tourist buses" .)
