"waste time," 1932; "make a mistake," 1941, from goof (n.). Goof off "loaf" is also from 1941. Related: Goofed; goofing.
1916, American English, "stupid person," perhaps a variant of English dialect goff "foolish clown" (1869), from 16c. goffe, probably from Middle French goffe "awkward, stupid," of uncertain origin. Or English goffe may be from Middle English goffen "speak in a frivolous manner," possibly from Old English gegaf "buffoonery," and gaffetung "scolding." Sense of "a blunder" is c.1954, probably influenced by gaffe.
Blunder, make a mistake, spoil. For example, I really goofed up and got all the dates wrong. This expression emerged in the military during World War II, along with the synonymous goof off. Quite often up is omitted, as in Sorry, I goofed. [Slang; c. 1940]