1709, "put aside, rejected," from verbal phrase cast off "discard, reject" (c. 1400), from cast (v.) + off (adv.). From 1741 as a noun, "person or thing abandoned as worthless or useless." Related" Cast-offs.
also faceoff, 1886 in sports (hockey, etc., originally lacrosse), from verbal phrase in a sports sense, attested from 1867 (see face (v.) + off (adv.)); the off perhaps is based on stand-off or similar constructions.