in football, "a kick of the ball as it is dropped from the hands and before it strikes the ground," 1845; from punt (v.).
"flat-bottomed, square-ended, mastless river boat," c. 1500, perhaps a local survival of late Old English punt, which probably is from British Latin ponto "flat-bottomed boat" (see OED), a kind of Gallic transport (Caesar), also "floating bridge" (Gellius), from Latin pontem (nominative pons) "bridge" (from PIE root *pent- "to tread, go;" see find (v.)). Or from or influenced by Old French cognate pont "large, flat boat." Compare pontoon.
"to kick a ball dropped from the hands before it hits the ground," 1845, first in a Rugby list of football rules, of obscure origin; perhaps from dialectal punt "to push, strike," alteration of Midlands dialect bunt "to push, butt with the head," of unknown origin, perhaps echoic (compare bunt).
Student slang meaning "give up, drop a course so as not to fail," 1970s, is because a U.S. football team punts when it cannot advance the ball. Related: Punted; punting.
"to propel as a punt is usually moved," by pushing with a pole against the bed of the body of water, 1816, from punt (n.2). Related: Punted; punting.