<p>The symmetric alternating direction method of multipliers (symmetric ADMM) is a flexible and efficient method for solving two-block optimization problems. However, the performance of symmetric ADMM degrades significantly when applied to large-scale problems. In this paper, we propose an accelerated stochastic symmetric ADMM (referred to ASS-ADMM) based on the symmetric ADMM framework, integrating variance reduced gradient estimator and over-relaxation technique for solving large-scale nonconvex optimization problems. Moreover, the Legendre function and the associated Bregman regularization are employed to relax the restrictive global Lipschitz smoothness assumption while simplifying subproblem computations. Under the assumption that the underlying function is semialgebraic without global Lipschitz smoothness, we prove that each bounded sequence generated by the ASS-ADMM converges to a critical point after a finite number of iterations, or almost surely satisfies the finite length property. In addition to bridging a theoretical gap in accelerated stochastic symmetric ADMM, numerical experiment on graph-guided fused lasso demonstrates the computational efficiency of the proposed method.</p>