A hallmark of the G1/S transition in budding yeast cell cycle is the proteolytic degradation of the B-type cyclin-Cdk stoichiometric inhibitor Sic1. Deleting SIC1 or altering Sic1 degradation dynamics increases genomic instability. Certain key facts about the parts of the G1/S circuitry are established: phosphorylation of Sic1 on multiple sites is necessary for its destruction, and both the upstream kinase Cln1/2-Cdk1 and the downstream kinase Clb5/6-Cdk1 can phosphorylate Sic1 in vitro with varied specificity, cooperativity, and processivity. However, how the system works as a whole is still controversial due to discrepancies between in vitro, in vivo, and theoretical studies. Here, by monitoring Sic1 destruction in real time in individual cells under various perturbations to the system, we provide a clear picture of how the circuitry functions as a switch in vivo. We show that Cln1/2-Cdk1 sets the proper timing of Sic1 destruction, but does not contribute to its destruction speed; thus, it acts only as a trigger. Sic1's inhibition target Clb5/6-Cdk1 controls the speed of Sic1 destruction through a double-negative feedback loop, ensuring a robust all-or-none transition for Clb5/6-Cdk1 activity. Furthermore, we demonstrate that the degradation of a single-phosphosite mutant of Sic1 is rapid and switch-like, just as the wild-type form. Our mathematical model confirms our understanding of the circuit and demonstrates that the substrate sharing between the two kinases is not a redundancy but a part of the design to overcome the trade-off between the timing and sharpness of Sic1 degradation. Our study provides direct mechanistic insight into the design features underlying the yeast G1/S switch.