This paper addresses the prescribed performance tracking control problem for the quadrotor slung load system under input saturation and partial-states constraints. Firstly, based on the method of barrier Lyapunov function (BLF), load position and linear velocity are constrained in the specified regions. Then, the fixed-time prescribed performance control (FTPPC) is introduced to the load attitude loop to confine the swing magnitude of the cable and simultaneously pledge the faster convergence speed. In addition, the hyperbolic tangent functions and the auxiliary systems are incorporated to alleviate the saturation nonlinearity effect. In virtue of the Lyapunov stability approach, all signals of the entire system are uniformly ultimately bounded and the constrained states remain in the specific performance boundaries. Finally, numerical simulation results attest to the effectiveness of the proposed backstepping control scheme.