Misuses of library APIs are pervasive and often lead to software bugs. Various static analysis tools have been proposed to detect API misuses. They often involve mining frequent patterns from a large number of correct API usage examples, which can be hard to obtain in practice. They also suffer from low precision due to an over-simplified assumption that a deviation from frequent usage patterns indicates a misuse. We make two observations on the detection of API misuses. First, API misuses can be represented as mutants of the corresponding correct usages. Second, whether a mutant will introduce a misuse can be validated via executing it against a test suite and analyzing the execution information. Based on these observations, we propose MutApi, the first approach to discovering API misuse patterns vis mutation analysis. To effectively mimic API misuses based on correct usages, we first design eight novel mutation operators according to the common characteristics of API misuses. MutApi generates mutants by applying these operators on client projects and collects mutant-killing tests as well as the concerned stack traces. Misuse patterns are discovered from the killed mutants that are prioritized according to their likelihood of causing API misuses based on the collected information. We applied MutApi on 73 popular Java APIs and 16 client projects for mutation analysis. The results show that MutApi can discover substantial API misuse patterns with a high precision of 0.78. It also achieves a recall of 0.49 on the MuBench benchmark, which significantly outperforms the state-of-the-art techniques.