Segment Anything Model (SAM), known for its remarkable zero-shot segmentation capabilities, has garnered significant attention in the community. Nevertheless, its performance is challenged when dealing with what we refer to as visually non-salient scenarios, where there is low contrast between the foreground and background. In these cases, existing methods often cannot capture accurate contours and fail to produce promising segmentation results. In this paper, we propose Visually Non-Salient SAM (VNS-SAM), aiming to enhance SAM's perception of visually non-salient scenarios while preserving its original zero-shot generalizability. We achieve this by effectively exploiting SAM's low-level features through two designs: Mask-Edge Token Interactive decoder and Non-Salient Feature Mining module. These designs help the SAM decoder gain a deeper understanding of non-salient characteristics with only marginal parameter increments and computational requirements. The additional parameters of VNS-SAM can be optimized within 4 hours, demonstrating its feasibility and practicality. In terms of data, we established VNS-SEG, a unified dataset for various VNS scenarios, with more than 35K images, in contrast to previous single-task adaptations. It is designed to make the model learn more robust VNS features and comprehensively benchmark the model's segmentation performance and generalizability on VNS scenarios. Extensive experiments across various VNS segmentation tasks demonstrate the superior performance of VNS-SAM, particularly under zero-shot settings, highlighting its potential for broad real-world applications. Codes and datasets are publicly available at https://guangqian-guo.github.io/VNS-SAM.