Born into a cycling family in Serbia, Radisa Cubric began racing when he was 10 years old, eventually joining the Yugoslavia National Team before advancing to larger team Montgomery Bell, which eventually became the United States Postal Service team. After participating in the Barcelona Olympic Games in 1992, he retired from pro racing in 1997, then becoming director for a variety of teams.

He most recently served as head coach and team manager for the Serbian National Team, then transitioning to a smaller team, Team CCN Metalac, to help develop young riders to the professional level.