Metasurface design often requires solving field distributions across varying structural parameters and frequencies, where neural operators offer a promising avenue for fast prediction. However, conventional neural operators have problems with degradation of the accuracy in multi-scale structural analysis. In this work, we propose a Generative Residual Enhanced Neural Operator (GRE-NO) framework that introduces a generative residual network to model the systematic bias of the main predictor. The core model retains the DeepONet architecture with both branch and trunk networks implemented using Fourier Neural Operators, combining strong generalization and efficient global representation. To handle the complexity of unbounded acoustic scattering problems, we integrate the Boundary Element Method (BEM) into data modeling and field computation, which reduces the problem dimensionality and enables training with samples at the ${10}^4$ scale. Numerical experiments on some 2D and 3D acoustic metasurface problems demonstrate that the developed GRE-NO achieves excellent accuracy in results with relative errors under 1% in this study, outperforming conventional neural networks in accuracy of prediction.