You and me chasing son with his cut food (5)
I believe the answer is:
sushi
'food' is the definition.
(sushi is a kind of food)
'you and me chasing son with his cut' is the wordplay.
'you and me' becomes 'us'.
'chasing' means one lot of letters go next to another (some letters chase after others).
'son' becomes 's' (genealogical abbreviation for son).
'with' means one lot of letters go next to another.
'cut' means to remove the last letter.
'his' with its last letter removed is 'hi'.
'us' after 's' is 'sus'.
'sus'+'hi'='SUSHI'
(Other definitions for sushi that I've seen before include "Japanese cuisine" , "Asian dish" , "Cold rice dish, often with raw fish" , "rice dishes" , "Asian food" .)