Joseph began his career alongside his older brother Francis at Division Three side Brentford, rejoining the club in October 1984 after having been released as a junior and dropped into non-league football with Southall. He made his senior debut on the final day of the 1984–85 season in a 1–1 draw with Millwall and attempted to establish himself as the club's first choice right back during the 1985–86 and 1986–87 seasons, before excelling in 1987–88 and winning Brentford's Players' Player of the Year award. His performances also saw him voted into the Division Three PFA Team of the Year, the first Brentford player to receive the accolade. He departed Griffin Park for a club record £150,000 fee in August 1988, having made 122 appearances and scored two goals for the Bees.
Joseph signed for Division One club and reigning FA Cup holders Wimbledon in August 1988 for a £150,000 fee. He began his time with the Dons as a regular but drifted out of contention by the 1993–94 season, making just 13 league appearances, before managing just three appearances in the following season and remaining absent for the entirety of 1995–96. Joseph was released in May 1996 after making 199 appearances without scoring.
On 2 March 1995, Joseph joined Division One side Millwall on loan until the end of the 1994–95 season. He made five appearances and scored no goals.
Joseph had a spell with Premier League club Chelsea during the early months of the 1996–97 season, making five appearances for the club's reserve team.
Joseph joined Division Three side Leyton Orient on a non-contract basis on 22 November 1996. He made 14 appearances before leaving Brisbane Road in February 1997.
Joseph moved back up to Division One to sign for West Bromwich Albion on non-contract terms 28 February 1997. He made just two substitute appearances the following month before departing the club at the end of the 1996–97 season.
Joseph returned to Leyton Orient on 3 August 1997. He was a regular pick during the 1997–98 and 1998–99 seasons and helped Orient to a sixth-place finish and a place in the 1999 Football League playoffs, but the Os were stopped on penalties in the semi-finals by Rotherham United. Joseph made just one appearance during the 1999–00 season and was released at the end of the campaign, after making 89 appearances across his two spells at Brisbane Road.
After his release from Leyton Orient, Joseph dropped into non-league football and spent time at King's Lynn, Leatherhead and two spells with former club Southall. He had two spells with AFC Wimbledon during the 2003–04 and 2004–05 seasons, becoming one of the first players to play for both Wimbledon and its phoenix club.
Joseph won two England B caps during the second half of the 1990–91 season, starting in wins over Iceland and Switzerland B.
Joseph's brother Francis and nephew Zak are also footballers. Prior to his return to professional football with Brentford in 1984, Joseph worked as a painter and decorator.Third Division PFA Team of the Year: 1987–88
Brentford Players' Player of the Year: 1987–88