Realizing beam cleanup using adaptive optics technique is an important research field of the high energy laser systems. To arrive at the aim of miniaturizing and low cost of the beam cleanup system, the method of wavefront distortion correction based on model-free optimization of the system performance metric is an appropriate scheme. This paper researches the application of the stochastic parallel gradient descent (SPGD) optimization algorithm on the beam cleanup system. Numerical simulations of the SPGD wavefront correction of phase aberrations commonly found in high energy laser beams were first carried out. Above this, an experimental 37-element adaptive optics beam cleanup system was set up and the influences of the two-sided perturbation method and the adaptive change of the iterative gain coefficient were studied on the convergence performance of the algorithm. The results of the numerical simulation and experiments verify the ability of the SPGD wavefront control method to correct different strengths of wavefront distortions and indicate the feasibility of the SPGD beam cleanup method.