WebAssembly (Wasm) smart contracts have shown growing popularity across blockchains (e.g., EOSIO) recently. Similar to Ethereum smart contracts, Wasm smart contracts suffer from various attacks exploiting their vulnerabilities. Even worse, few developers released the source code of their Wasm smart contracts for security review, raising the bar for uncovering vulnerable contracts. Although a few approaches have been proposed to detect vulnerable Wasm smart contracts, they have several major limitations, e.g., low code coverage, low accuracy and lack of scalability, unable to produce exploit payloads, etc. To fill the gap, in this paper, we design and develop WASAI, a new concolic fuzzer for uncovering vulnerabilities in Wasm smart contract after tackling several challenging issues. We conduct extensive experiments to evaluate WASAI, and the results show that it outperforms the state-of-the-art methods. For example, it achieves 2x code coverage than the baselines and surpasses them in detection accuracy, with an F1-measure of 99.2%. Moreover, WASAI can handle complicated contracts (e.g., contracts with obfuscation and sophisticated verification). Applying WASAI to 991 deployed smart contracts in the wild, we find that over 70% of smart contracts are vulnerable. By the time of this study, over 300 vulnerable contracts have not been patched and are still operating on the EOSIO Mainnet. One fake EOS vulnerability reported to the EOSIO ecosystem was recently assigned a CVE identifier (CVE-2022-27134).