With the rapid advance of spatial multi-omics technologies, it has become possible to simultaneously profile transcripts, proteins and chromatin states at their native spatial coordinates, thereby uncovering molecular architecture that transcends any single-omics perspective. However, the resulting data matrices are often highly sparse and suffer from unstable dimensionality. Graph-based neural methods capture only local neighborhood information, whereas conventional Transformers, although capable of modelling long-range dependencies, incur prohibitive computational costs on such data. To overcome these limitations, we propose TLAGC—a Taylor-Linear-Attention-Guided Graph Convolutional framework that couples a Taylor-expanded linear attention (TLA) mechanism with graph convolutional networks. By eliminating the soft-max operation and linking the LocalGCN via residual connections, TLA preserves local structural information while enabling the integration of global and local contexts, thereby alleviating ineffective information propagation between spatially distant yet transcriptionally similar regions. Theoretical analysis confirms that TLA indeed reduces computational complexity, and extensive experiments on multiple spatial multi-omics benchmarks demonstrate that TLAGC consistently outperforms state-of-the-art baselines in delineating spatial domains.