Spatially resolved omics technologies reveal the spatial organization of cells in various biological systems. Integrative and comparative analyses of spatial omics data depend on proper slice alignment, which should take both omics profiles and spatial context into account. Here we propose SLAT (Spatially-Linked Alignment Tool), a graph-based algorithm for efficient and effective alignment of spatial omics data. Adopting a graph adversarial matching strategy, SLAT is the first algorithm capable of aligning heterogenous spatial data across distinct technologies and modalities. Systematic benchmarks demonstrate SLAT's superior precision, robustness, and speed compared to existing methods. Applications to multiple real-world datasets further show SLAT's utility in enhancing cell-typing resolution, integrating multiple modalities for regulatory inference, and mapping fine-scale spatial-temporal changes during development. The full SLAT package is available at https://github.com/gao-lab/SLAT.