Serving as the first touch point for users to the cryptocurrency world, cryptocurrency wallets allow users to manage, receive, and transmit digital assets on blockchain networks and interact with emerging decentralized finance (DeFi) applications. Unfortunately, cryptocurrency wallets have always been the prime targets for attackers, and incidents of wallet breaches have been reported from time to time. Although some recent studies have characterized the vulnerabilities and scams related to wallets, they have generally been characterized in coarse granularity, overlooking potential risks inherent in detailed designs of cryptocurrency wallets, especially from perspectives including user interaction and advanced features. To fill the void, in this paper, we present a fine-grained security analysis on browser-based cryptocurrency wallets. To pinpoint security issues of components in wallets, we design WalletProbe, a mutation-based testing framework based on visual-level oracles. We have identified 13 attack vectors that can be abused by attackers to exploit cryptocurrency wallets and exposed 21 concrete attack strategies. By applying WalletProbe on 39 widely-adopted browser-based wallet extensions, we astonishingly figure out all of them can be abused to steal crypto assets from innocent users. Identified potential attack vectors were reported to wallet developers timely and 26 issues have been patched already. It is, hence, urgent for our community to take action to mitigate threats related to cryptocurrency wallets. We promise to release all code and data to promote the development of the community.