1916, "stupid person," American English, perhaps a variant of English dialect goff "foolish clown" (1869), from 16c. goffe, probably from Middle French goffe "awkward, stupid," which is of uncertain origin. Or English goffe may be from Middle English goffen "speak in a frivolous manner," which is possibly from Old English gegaf "buffoonery," and gaffetung "scolding." Sense of "a blunder" is c. 1954, probably influenced by gaffe. Also compare goofer, goopher which appears in representations of African-American dialect from 1887 in the sense of "a curse, spell," probably from an African word.
1922, "waste time;" 1941; "make a mistake," from goof (n.). Goof off is from 1941, originally World War II armed forces, "to make a mistake at drill;" by 1945 as "to loaf, waste time," also as a noun for one who does this. Related: Goofed; goofing.