Separated half of dishes, cracked (9)
I believe the answer is:
dissolved
'separated' is the definition.
'half of dishes cracked' is the wordplay.
'half of' indicates taking half.
'cracked' becomes 'solved' (like a police case or a puzzle).
'dishes' halved is 'dis'.
'dis'+'solved'='DISSOLVED'
(Other definitions for dissolved that I've seen before include "Disbanded or broke up" , "Melted" , "Concluded" , "Reduced to liquid form" .)