Dish cut into pieces the old American served up (4,4)
I believe the answer is:
chop suey
'dish' is the definition.
(chop suey is a kind of dish)
'cut into pieces the old american served up' is the wordplay.
'cut into pieces' becomes 'chop' ('chop' can be a synonym of 'cut into pieces').
'the old' becomes 'ye'.
'american' becomes 'us'.
'served up' shows that the letters should be reversed in order.
'ye'+'us'='yeus'
'yeus' written backwards gives 'suey'.
'chop'+'suey'='CHOP SUEY'
(Other definitions for chop suey that I've seen before include "Might he copy us badly in this Chinese-style dish?" , "Chinese dish of stir-fried meat or fish with vegetables, originally created in the US" , "Chinese dish of meat pieces, rice and vegetables" , "Cue Sophy into Chinese dish of meat, rice and vegetables" .)