While the Segment Anything Model (SAM) transforms interactive segmentation with zero-shot abilities, its inherent vulnerabilities present a single-point risk, potentially leading to the failure of downstream applications. Proactively evaluating these transferable vulnerabilities is thus imperative. Prior adversarial attacks on SAM often present limited transferability due to insufficient exploration of common weakness across domains. To address this, we propose a novel method, Vertex-Refining Simplicial Complex Attack (VeSCA), generating transferable adversarial examples by explicitly characterizing the shared vulnerable regions between SAM and downstream models through a parametric simplicial complex. Our goal is to identify such complexes within adversarially potent regions by iterative vertex-wise refinement.A lightweight domain re-adaptation strategy is introduced to bridge domain divergence using minimal reference data. Notably, VeSCA leverages only the encoder of SAM, which mitigates overfitting issue, and generates consistently transferable adversarial examples by random simplicial complex sampling. Extensive experiments demonstrate that VeSCA achieves performance improved by 12.7\% compared to state-of-the-art methods across three downstream model categories across five domain-specific datasets. Our findings further highlight the downstream model risks posed by SAM’s vulnerabilities.