The C32 was designed by Matt Morris, Pierre Waché, and Willem Toet. Its most striking visual feature was a pair of distinctly narrow sidepods, a concept reportedly inspired by Sergio Pérez's 2011 Monaco Grand Prix crash, in which a side-on barrier impact crushed one sidepod and prompted the team to investigate how slim a sidepod could be made in practice. Achieving the narrow profile required a complete internal reconfiguration of the car's layout. Compared to the outgoing Sauber C31, the C32 adopted a lower, smooth nose profile, abandoning the stepped nose design that had been widespread on the 2012 grid. The livery also changed significantly, moving from a white base to a grey scheme with black, red, and white accents; sponsors included Claro, Telcel, Telmex, Oerlikon, NEC, and Certina, with Chelsea FC returning for a second year.
The C32's debut at the Australian Grand Prix was troubled: Hülkenberg qualified eleventh but could not start after a fuel system leak was discovered, while Gutiérrez qualified eighteenth and finished thirteenth, the highest-placed rookie in the race. The Malaysian Grand Prix provided Sauber's first points of the year, with Hülkenberg finishing eighth.
Form was inconsistent through the opening half of the season. Both drivers retired due to accidents in Canada, and the Hungarian and Belgian Grands Prix yielded no points. However, the Italian Grand Prix at Monza provided a highlight: Hülkenberg qualified a remarkable third and converted it into fifth place at the flag, the team's best result since Kamui Kobayashi's third-place podium at the 2012 Japanese Grand Prix. A fourth-place finish in Korea followed shortly after, and Gutiérrez equalled his best race result with eleventh in the same event.
At the Japanese Grand Prix, Gutiérrez scored seventh place — his sole points finish of the entire season. Hülkenberg ultimately accumulated the bulk of Sauber's points, ending the year with multiple top-ten finishes in the second half of the season. The team finished seventh in the Constructors' Championship with 57 points, a significant step back from the C31's sixth-place standing with 126 points and four podiums in 2012.
The C32 resurfaced in a ceremonial role several years after its competitive life ended. In 2018 it was used during the launch presentation of the Sauber C37, and later that year it was demonstrated at the Milano Festival by Marcus Ericsson and Charles Leclerc. In 2025, Gabriel Bortoleto drove the C32 at the Goodwood Festival of Speed, the car wearing the livery of the then-current 2025 Sauber C45.
The 2013 season marked a transitional period for the Swiss team. While the C32's narrow-sidepod concept drew genuine engineering interest, the car's pace in qualifying was not reliably converted into race results, and midfield competition meant that points often came in clusters. Hülkenberg's Monza qualifying performance and race result remained the headline achievement of the C32's single competitive season.