Lesion segmentation is a fundamental task in medical image processing, often facing the challenge of subtle lesions. It is important to detect these lesions, even though they can be difficult to identify. Convolutional neural networks, an effective method in medical image processing, often ignore the relationship between lesions, leading to topological errors during training. To tackle topological errors, move is made from pixel‐level to hypergraph representations. Hypergraphs can model lesions as vertices connected by hyperedges, capturing the topology between lesions. This paper introduces a novel dynamic hypergraph learning strategy called DHLS. DHLS allows for the dynamic construction of hypergraphs contingent upon input vertex variations. A hypergraph global‐aware segmentation network, termed HGSNet, is further proposed. HGSNet can capture the key high‐order structure information, which is able to enhance global topology expression. Additionally, a composite loss function is introduced. The function emphasizes the global aspect and the boundary of segmentation regions. The experimental setup compared HGSNet with other advanced models on medical image datasets from various organs. The results demonstrate that HGSNet outperforms other models and achieves state‐of‐the‐art performance on three public datasets.