The proliferation of blockchain-backed cryptocurrencies has sparked the need for cross-chain exchanges of diverse digital assets. Unfortunately, current exchanges suffer from high on-chain verification costs, weak threat models of central trusted parties, or synchronous requirements, making them impractical for currency trading applications. In this paper, we present MERCURY, a practical cryptocurrency exchange that is trust-minimized and efficient without online-client requirements. MERCURY leverages Trusted Execution Environments (TEEs) to shield participants from malicious behaviors, eliminating the reliance on trusted participants and making on-chain verification efficient. Despite the simple idea, building a practical TEE-assisted cross-chain exchange is challenging due to the security and unavailability issues of TEEs. MERCURY tackles the unavailability problem of TEEs by implementing an efficient challenge-response mechanism executed on smart contracts. Furthermore, MERCURY utilizes a lightweight transaction verification mechanism and adopts multiple optimizations to reduce on-chain costs. Comparative evaluations with XClaim, ZK-bridge, and Tesseract demonstrate that MERCURY significantly reduces on-chain costs by approximately 67.87%, 45.01%, and 47.70%, respectively.