In real-world applications, we encounter various types of graph data, and Graph Neural Networks (GNNs) are powerful tools for processing these graphs. However, despite numerous GNN architectures being developed, challenges such as the homogeneity assumption and over-smoothing persist, limiting their generalization and applicability. Furthermore, learning from diverse types and semantic information in graphs still heavily depends on manually designed networks. To address these limitations, we introduce AutoSGNN, an automatic propagation mechanism discovery framework for spectral graph neural networks. AutoSGNN integrates large language models with evolutionary strategies to automatically generate adaptable spectral GNNs tailored to different graph types. By employing a unified architecture for spectral GNNs, LLMs are guided to learn crucial components such as feature fitting terms, graph Laplacian regularization terms, and aggregation terms. This approach enables the design of optimal spectral GNNs for specific graph data while providing a clear design philosophy for network architecture. We conducted extensive experiments on nine widely-used datasets, including both homophilic and heterophilic graphs. The results demonstrate that AutoSGNN significantly outperforms existing state-of-the-art spectral GNN methods and neural architecture search approaches in terms of both performance and efficiency.