Cross-chain bridges are essential decentralized applications (DApps) to facilitate interoperability between different blockchain networks. Unlike regular DApps, the functionality of cross-chain bridges relies on the collaboration of information both on and off the chain, which exposes them to a wider risk of attacks. According to our statistics, attacks on cross-chain bridges have resulted in losses of nearly 4.3 billion dollars since 2021. Therefore, it is particularly necessary to understand and detect attacks on cross-chain bridges. In this paper, we collect the largest number of cross-chain bridge attack incidents to date, including 49 attacks that occurred between June 2021 and September 2024. Our analysis reveal that attacks against cross-chain business logic cause significantly more damage than those that do not. These cross-chain attacks exhibit different patterns compared to normal transactions in terms of call structure, which effectively indicates potential attack behaviors. Given the significant losses in these cases and the scarcity of related research, this paper aims to detect attacks against cross-chain business logic, and propose the BridgeGuard tool. Specifically, BridgeGuard models cross-chain transactions from a graph perspective, and employs a two-stage detection framework comprising global and local graph mining to identify attack patterns in cross-chain transactions. We conduct multiple experiments on the datasets with 203 attack transactions and 40,000 normal cross-chain transactions. The results show that BridgeGuard's reported recall score is 36.32\% higher than that of state-of-the-art tools and can detect unknown attack transactions.