This paper investigates the problem of cooperative payload delivery by two quadrotors with a novel “Y”-shaped cable that improves payload carrying and dropping efficiency. Compared with the existing “V”-shaped suspension, the proposed suspension method adds another payload swing degree of freedom to the quadrotor–payload system, making the modeling and control of such a system more challenging. In the modeling, the payload swing motion is decomposed into a forward–backward process and a lateral process, and the swing motion is then transmitted to the dynamics of the two quadrotors by converting it into disturbance cable pulling forces. A novel guidance and control framework is proposed, where a guidance law is designed to not only achieve formation transformation but also generate a local reference for the quadrotor, which does not have access to the global reference, based on which a cooperative controller is developed by incorporating an uncertainty and disturbance estimator to actively compensate for payload swing disturbance to achieve the desired formation trajectory tracking performance. A singular perturbation theory-based analysis shows that the proposed parameter mapping method, which unifies the parameter tuning of different control channels, allows us to tune a single parameter, $\epsilon$, to quantitatively enhance both the formation control performance and system robustness. Simulation results verify the effectiveness of the proposed approach in different scenarios.