also cutoff, 1640s, "act of cutting off," also "portion cut off," from verbal phrase cut off (see cut (v.) + off (adv.)). Sense of "new and shorter channel formed on a river" (especially the Mississippi) is from 1773; of road that cut off or shorten a route, from 1806; of clothing (adj.), from 1840. Cutoffs "jeans or other long pants trimmed down to be shorts" is by 1967.
The verbal phrase is attested from late 14c. as "detach by cutting;" from 1570s as "exclude from access" and "bring to an abrupt end;" and from 1590s as "intercept, stop the flow or passage of."