When Sauber set out to build the C7, they chose to evolve the architecture of the SHS C6 rather than design an entirely new car. The BMW M88 engine was retained in the hope that refinements to the chassis would unlock more of the unit's potential. The car was completed in time for the 1983 World Sportscar Championship season.
The C7 made its debut at the 1983 24 Hours of Le Mans, the fourth round of the World Sportscar Championship that year. Despite competing against the dominant Porsche 956s, which filled the first eight positions at the finish, the C7 placed ninth overall — a result that demonstrated genuine competitiveness given the strength of the field. The car appeared once more during 1983, at the round at Fuji, where it finished tenth overall.
After those two outings, development of the sole C7 chassis ceased. The 1983 season had been too brief and too limited in scope to justify further investment, and Sauber announced a hiatus from sportscar racing.
With the team stepping back, Sauber sold the C7 chassis to Fomfor Racing, an outfit from El Salvador. Fomfor transported the car to the United States to compete in the 1984 IMSA Camel GT championship, retaining the BMW M88 engine for the opening five rounds of the season. The team's best result in that period was seventh place at Road Atlanta. Fomfor subsequently withdrew from the championship before its conclusion, returning only for the season finale at Daytona International Speedway. By that point the BMW straight-six had been replaced by a Chevrolet 6.0-litre V8, and the team finished eleventh overall.
Fomfor attempted to continue racing the C7 into 1985 but managed only two entries. The first was at Miami for an IMSA round, where the car failed to finish. The second was at Mosport for a World Sportscar Championship round, where the team placed seventh overall. The squad folded shortly afterwards, bringing the C7's active racing life to a close after just over a full season of competition.
The C7's most lasting significance was that it served as the design starting point for the Sauber C8, which followed after the team ended its hiatus and entered a partnership with Mercedes-Benz. The C8 carried over a large number of structural and conceptual traits from the C7, adapting them to accept the larger Mercedes turbocharged V8. In this way the C7, for all its brevity, formed the technical foundation from which the far more successful Sauber-Mercedes programme of the late 1980s would grow.