Cut sandwiches near Detroit (6)
I believe the answer is:
motown
'detroit' is the definition.
(Detroit is nicknamed Motown)
'cut sandwiches near' is the wordplay.
'cut' becomes 'mown' (past tense of 'mow').
'sandwiches' is an insertion indicator (goes on either side like a sandwich).
'near' becomes 'to' (to can mean near or close to).
'mown' going around 'to' is 'MOTOWN'.
(Other definitions for motown that I've seen before include "Tamla -, US soul music record label" , "Tom won (anag) - music" , "music from America" , "Genre of music originally from Detroit" , "Detroit musical style" .)