The global semiconductor supply chain (SSC) represents the central nervous system of the modern digital economy, yet its hyper-specialized and geographically concentrated structure renders it profoundly vulnerable to systemic disruptions. Recent events, such as the COVID-19 pandemic and escalating geopolitical tensions, have exposed the limitations of traditional, reactive risk management paradigms. This paper addresses a critical research gap by proposing a proactive methodology for resilience engineering: a stress testing framework adapted from the financial industry. The framework is built upon a high-fidelity "Geopolitical Digital Twin" of the supply chain, which allows for the simulation of severe but plausible disruption scenarios. This paper's primary contribution is a rigorous, quantitative methodology for assessing systemic vulnerabilities, quantifying the cascading impacts of disruptions, and evaluating the efficacy of various mitigation strategies. A case application simulating a 90-day geopolitical blockade of the Taiwan Strait is presented. The results quantify the catastrophic ripple effects on global industries, particularly automotive and consumer electronics, and reveal critical second-order chokepoints in raw materials and logistics. Furthermore, the analysis provides a data-driven evaluation of mitigation levers, such as strategic stockpiling and the diversification of fabrication capacity through initiatives like the U.S. and E.U. CHIPS Acts. The findings offer significant implications for both corporate strategy and public policy, providing a robust analytical tool to navigate the trade-offs between efficiency and resilience in an era of increasing uncertainty