Meaning "from one's own or accustomed place" is from c. 1300; that of "from one state or condition to another" is from mid-14c.; that of "from one's possession (give away, throw away) is from c. 1400. Colloquial use for "without delay" (fire away, also right away) is from earlier sense of "onward in time" (16c.). Meaning "at such a distance" (a mile away) is by 1712. Intensive use (as in away back) is American English, attested by 1818. Of sporting events played at the other team's field or court, by 1893.
of coats, "cut back from the waist," 1841, from the verbal phrase; see cut (v.) + away. As a noun, "coat cut back from the waist," by 1849. In reference to models, drawings, etc., of which a part is cut away to reveal the interior, by 1946. The verbal phrase is from c. 1300 as "cut (something) off or away."