To solve the problems of the difficulty in adjusting parameters in real time and the convergence speed being slow in the traditional stochastic parallel gradient descent (SPGD) algorithm, this study proposes an efficient SPGD algorithm based on adaptive gain and joint index optimization and establishes a numerical simulation model of this algorithm. The proposed algorithm is used for the beam cleaning of kilowatt-class slab lasers. Simulation results show that compared with the traditional SPGD algorithm, the proposed algorithm does not require a parameter adjustment, and the convergence speed and convergence effect are significantly improved. Furthermore, in the beam purification experiment of the kilowatt-class slab laser, the laser beam quality β is optimized from 7.89 to 1.95 herein.