"submissive, humble, lowly," 1570s, from Latin demissus "let down, lowered," past participle of demittere, literally "to send down," from de "down" (see de-) + mittere "to let go, send, release" (see mission).
active word-forming element in English and in many verbs inherited from French and Latin, from Latin de "down, down from, from, off; concerning" (see de), also used as a prefix in Latin, usually meaning "down, off, away, from among, down from," but also "down to the bottom, totally" hence "completely" (intensive or completive), which is its sense in many English words.
As a Latin prefix it also had the function of undoing or reversing a verb's action, and hence it came to be used as a pure privative — "not, do the opposite of, undo" — which is its primary function as a living prefix in English, as in defrost (1895), defuse (1943), de-escalate (1964), etc. In some cases, a reduced form of dis-.
1590s, "a sending abroad" (as an agent), originally of Jesuits, from Latin missionem (nominative missio) "act of sending, a dispatching; a release, a setting at liberty; discharge from service, dismissal," noun of action from past-participle stem of mittere "to release, let go; send, throw," which de Vaan traces to a PIE *m(e)ith- "to exchange, remove," also source of Sanskrit methete, mimetha "to become hostile, quarrel," Gothic in-maidjan "to change;" he writes, "From original 'exchange', the meaning developed to 'give, bestow' ... and 'let go, send'."
Meaning "an organized effort for the spread of religion or for enlightenment of a community" is by 1640s; that of "a missionary post or station" is by 1769. The diplomatic sense of "body of persons sent to a foreign land on commercial or political business" is from 1620s; in American English, sometimes "a foreign legation or embassy, the office of a foreign envoy" (1805).
General sense of "that for which one is sent or commissioned" is from 1670s; meaning "that for which a person or thing is destined" (as in man on a mission, one's mission in life) is by 1805. Meaning "dispatch of an aircraft on a military operation" (by 1929, American English) was extended to spacecraft flights (1962), hence, mission control "team on the ground responsible for directing a spacecraft and its crew" (1964). As a style of furniture, said to be imitative of furniture in the buildings of original Spanish missions to western North America, it is attested from 1900.