Incision segmentation plays a crucial role in clinical surgical automation yet remains an overlooked target. In recent years, the Segment Anything Model (SAM) has demonstrated impressive prompt-based segmentation capabilities, benefiting from extensive pre-training on large datasets. However, due to the complex morphology of incisions and background interference, SAM with existing prompt modes, such as points and bounding boxes, exhibits several limitations. Firstly, point prompts cannot represent the shape information of incisions. Affected by background interference such as bloodstains and surgical instruments, points struggle to effectively guide the model. Secondly, while bounding box prompts contain some spatial information, their relatively coarse structure makes it difficult to capture the complex morphology of incisions. To address these issues, we present the Geometric Informed Polygon Prompt for Incision Segmentation (GPIS), consisting of Polygon Prompt Method (PP) and Geometric Information Enhancement Module (GIE). The PP method introduces a new polygon prompt mode, which refines the prompt structure to better capture the complex morphology of incisions and effectively reduce ambiguity. Furthermore, the GIE module incorporates distance features, mapping polygons into dense prompts enriched with SDF to compensate for missing geometric information. Extensive experiments on the incision segmentation task demonstrate the effectiveness and superiority of GPIS over other prompt modes.