"to destroy," 1958, probably a back-formation from destruction in the jargon of U.S. aerospace and defense workers to refer to deliberate destruction of a missile in flight by a friendly agent; popularized 1966 in form self-destruct in the voice-over at the beginning of TV spy drama "Mission Impossible." OED records an isolated use of destructed from 17c., in this case probably from Latin destructus, past participle of destruere.
in reference to things, "destroy itself automatically;" see self- + destruct, apparently first attested in the U.S. television series "Mission Impossible" (1966). Self-destructive "having the property of annulling itself" is recorded from 1650s, and self-destruction "destruction of oneself, suicide" is attested from 1580s; self-destroying (n.) is from 1610s.
"causing destruction, tending to destroy," late 15c. (Caxton), from Old French destructif (14c.), from Late Latin destructivus, from destruct-, past-participle stem of Latin destruere "to tear down, demolish" (see destroy). Related: Destructively; destructiveness.