A native of Dayton, Ohio, Raimey twice won state championships in the low hurdles and long jump.

He played college football as a halfback and defensive back for the University of Michigan and was the team's leading scorer for three consecutive years from 1960 to 1962.

He led Wilson to the Ohio Class A track championship in 1958, placing first in the broad jump and 180-yard low hurdles.

[6] As a sophomore in 1960, Raimey started three games at the halfback position,[7] gained 342 net rushing yards in 62 attempts, and led the team in scoring with six touchdowns.

Head coach Bump Elliott noted: "I don't believe people know how well Dave plays on defense.

For the season, he led Michigan with 496 rushing yards on 99 attempts and was the team's leading scorer for the second consecutive year with six touchdowns.

[12] The Daily further noted that Raimey had a "rare combination of power and speed to make him a breakaway threat from any point on the field.

[14] Raimey played the 1962 season with a harness over his shoulders to protect an injury that was diagnosed as bone chips.

He turned down an offer from the Browns,[16] instead signing with the Winnipeg Blue Bombers of the Canadian Football League for a $5,000 bonus and a three-year contract.

[21] Columnist Don Blanchard of the Winnipeg Free Press wrote in August 1965 that Raimey was "operating like the best halfback in the league" since Leo Lewis a decade earlier.

[25] The team advanced to the 1965 Grey Cup game, known as the "Wind Bowl", where they lost to the Hamilton Tiger-Cats.

[21] At the end of the season, he was selected as a CFL offensive all-star;[27] he also received the Blue Bombers' Most Outstanding Player award.

His total of 2,278 all-purpose yards was a career high, and he was selected as a Western Conference all-star for the fourth consecutive season.

[28] In July 1969, during a practice session, Raimey had an angry "exchange of words" with Winnipeg quarterback John Schneider.

[29] A short time later, Raimey was traded to the Toronto Argonauts in exchange for another former Michigan player, Wally Gabler.

[21] His season ended in late October when he tore ligaments in his left leg during a game against Hamilton.

[32] In June 1970, Toronto team physicians declared Raimmey's knee fit, but he reported that it still hurt and even rattled at times.

[39] As of December 2000, Raimey was living in Dayton, Ohio, where he was renovating a storefront in the city's Wright-Dunbar Historic District.