Abstract: Against the backdrop of the 2026 Strait of Hormuz blockade crisis, this study focuses on the impacts of supply disruptions in two oil and gas industrial by-products, sulfur and petroleum coke, on critical mineral supply chains, and reveals the problem of “functional chokepoints” that has been overlooked in conventional critical mineral risk assessment frameworks. The results show that, although sulfur is not classified as a critical mineral, it is deeply embedded in the hydrometallurgical refining systems of copper, cobalt, and nickel as a feedstock for sulfuric acid production. Disruptions to Middle Eastern sulfur supply would directly exacerbate the risk of production shutdowns in copper and cobalt operations in the Democratic Republic of the Congo, while increasing the cost and output uncertainty of Indonesia’s mixed hydroxide precipitate hydrometallurgical production. Petroleum coke, in turn, supports primary aluminum production through the calcined coke and carbon anode segments. Disruptions to the Strait of Hormuz would therefore interact with interruptions in alumina transportation, generating multiple shocks to global aluminum supply. This study further argues that sulfur and petroleum coke share a common feature: their by-product nature limits independent supply elasticity, while their trade routes are highly concentrated around the Persian Gulf and the Strait of Hormuz. Once exposed to geopolitical conflict, these characteristics may generate cross-industrial, concurrent, and systemic risks. From the perspective of “chokepoint economics,” this study recommends establishing a national-level security assessment system for industrial auxiliary materials, incorporating the identification of functional constraint nodes into resource security analysis frameworks, constructing a quantitative matrix of dependency between auxiliary materials and downstream industries, and evaluating the systemic amplification effects arising from the nesting of constraint nodes and transportation chokepoints. At the multilateral level, it further calls for the establishment of a global supply chain security mechanism centered on critical supply nodes.