Large language models based on Mixture-of-Experts have achieved substantial gains in efficiency and scalability, yet their architectural uniqueness introduces underexplored safety alignment challenges. Existing safety alignment strategies, predominantly designed for dense models, are ill-suited to address MoE-specific vulnerabilities. In this work, we formalize and systematically study MoE model's positional vulnerability - the phenomenon where safety-aligned behaviors rely on specific expert modules, revealing critical risks inherent to MoE architectures. To this end, we present SAFEx, an analytical framework that robustly identifies, characterizes, and validates the safety-critical experts using a novel Stability-based Expert Selection (SES) algorithm. Notably, our approach enables the explicit decomposition of safety-critical experts into distinct functional groups, including those responsible for harmful content detection and those controlling safe response generation. Extensive experiments on mainstream MoE models, such as the recently released Qwen3-MoE, demonstrated that their intrinsic safety mechanisms heavily rely on a small subset of positional experts. Disabling these experts significantly compromised the models' ability to refuse harmful requests. For Qwen3-MoE with 6144 experts (in the FNN layer), we find that disabling as few as 12 identified safety-critical experts can cause the refusal rate to drop by 22%, demonstrating the disproportionate impact of a small set of experts on overall model safety.