early 14c., des, dys, plural of dy (see die (n.)), altered 14c. to dyse, dyce, and 15c. to dice. "As in pence, the plural s retains its original breath sound, probably because these words were not felt as ordinary plurals, but as collective words" [OED]. Sometimes used as singular 1400-1700.
"to cut into cubes," late 14c., from dice (n.). Meaning "to play at dice" is from early 15c. Related: Diced; dicing.