Properly integrating spatially resolved transcriptomics (SRT) generated from different batches into a unified gene-spatial coordinate system could enable the construction of a comprehensive spatial transcriptome atlas. Here, we propose SPIRAL, consisting of two consecutive modules: SPIRAL-integration, with graph domain adaptation-based data integration, and SPIRAL-alignment, with cluster-aware optimal transport-based coordination alignment. We verify SPIRAL with both synthetic and real SRT datasets. By encoding spatial correlations to gene expressions, SPIRAL-integration surpasses state-of-the-art methods in both batch effect removal and joint spatial domain identification. By aligning spots cluster-wise, SPIRAL-alignment achieves more accurate coordinate alignments than existing methods.