Tire blowout can lead to vehicle instability and yawing, especially when the vehicle is traveling at high speeds, which may cause severe traffic accidents. To address this issue, modifications were made to the Magic Formula tire model, the two-degree-of-freedom vehicle model, and the lateral stability indices for tire blowout scenarios. The phase plane theory was employed to analyze the cause of vehicle yawing after the tire blowout stabilizes. A hierarchical controller based on Model Predictive Control (MPC) is proposed for vehicle's stability and trajectory tracking after tire blowout. The upper-layer controller adopts the MPC strategy, which ensures the vehicle's path-tracking performance by controlling the front wheel steering angle and additional yaw moment. The lower-layer controller distributes the additional yaw moment output by the upper-layer controller to the rear wheel steering angle and motor torque using tire utilization rate, thereby improving the driving stability of the vehicle. Simulation results demonstrate that compared with the MPC control strategy alone, the proposed hierarchical controller can reduce the lateral error while ensuring vehicle stability. The research findings hold significant theoretical value and engineering significance for both stability control and path-tracking control of vehicles after tire blowout.