Austenite stainless steel of type 304 is one of the most difficult materials to process. During the machining process, parts easily generate higher surface residual stress in cutting direction (CD) and production costs. To solve the problem, a multi-objective optimization method that combined Dung Beetle Optimizer-Back Propagation Neural Network (DBO-BPNN) and Improved Particle Swarm Optimization (IPSO) algorithm was adopted. Firstly, BPNN, Genetic Algorithm-Back Propagation Neural Network (GA-BPNN) and DBO-BPNN were established to map the nonlinear relationship between surface residual stress in CD and turning parameters. Secondly, a dataset of surface residual stress in CD and material removal rate under different turning parameters was obtained through finite element method (FEM) turning simulation. The dataset was applied into neural network to establish a nonlinear mapping relationship between turning parameters and surface residual stress in CD. The turning parameters are used as variables, the surface residual stress in CD and material removal rate are applied as objective functions. The optimal Pareto solution set of the surface residual stress in CD and material removal rate was acquired by combining DBO-BPNN and IPSO. Finally, turning experiments were designed to verify the accuracy of the turning simulation. The study shows that the surface residual stress in CD decreased by 38.47%, and the material removal rate increased by 91.69%.