Morphological differences and dense spatial relations of organs make multi-organ segmentation challenging. Current segmentation networks, primarily based on CNNs and Transformers, represent organs by aggregating information within fixed regions. However, aggregated representations often fail to accurately describe the shape differences and spatial relationships of multi-organs, which leads to imprecise morphological modeling and ambiguous boundary representation. In response, we propose a novel multi-organ segmentation network via dynamic graph reconstruction, called DGRNet. Unlike existing approaches, DGRNet employs a graph-based paradigm to reconstruct multi-organs and leverages the topological flexibility of graphs to represent irregular organ morphology. Based on graph connectivity, the precise information interaction makes more efficient multi-organ modeling. Furthermore, DGRNet introduces a category-aware guidance mechanism that utilizes organ category-specific priors to explicitly define inter-organ boundaries, addressing the issue of ambiguous margin delineation in multi-organ regions. We conducted extensive experiments on five datasets (including CT and MRI), showing that DGRNet outperforms state-of-the-art methods and models complex multi-organ areas better, highlighting its effectiveness and robustness.