"exceed in any excess of evil," from Shakespeare's it out-Herods Herod in Hamlet's instruction to the players in "Hamlet" Act III, Scene II. Shakespeare used the same construction elsewhere ("All's Well that Ends Well" has out-villain'd villany). The phrase reflects the image of Herod as stock braggart and bully in old religious drama. The form of the phrase was widely imitated 19c. and extended to any excessive behavior.
Oh, it offends me to the soul to hear a robustious periwig-pated fellow tear a passion to tatters, to very rags, to split the ears of the groundlings, who for the most part are capable of nothing but inexplicable dumb-shows and noise: I would have such a fellow whipped for o'erdoing Termagant; it out-herods Herod: pray you, avoid it. ["Hamlet"]
1957, "make an electronic noise" (originally in reference to Sputnik), from bleep (n.); specific sense of "edit a sound over a word deemed unfit for broadcast" is from 1964. Related: Bleeped; bleeping. Bleeper "pager consisting of a mini radio receiver that announces reception of signals by emitting a bleeping noise" is from 1964.
late 14c., redacten, "combine in a unity;" c. 1400, "compile, arrange" (laws, codes, etc.); early 15c., "bring into organized form;" from Latin redactus, past participle of redigere "to drive back, force back; bring back; collect, call in; bring down, reduce to a certain state," from red- "back, again" (see re-) + agere "to set in motion, drive, do, perform" (from PIE root *ag- "to drive, draw out or forth, move").
The specific meaning "arrange, edit, bring into presentable literary form" is from 1851. Also in Middle English "to reduce" (to ashes, powder, etc.), early 15c. Related: Redacted; redacting; redactor; rédacteur.