API error-handling specifications are often not documented, necessitating automated specification mining. Automated mining of error-handling specifications is challenging for procedural languages such as C, which lack explicit exception-handling mechanisms. Due to the lack of explicit exception handling, error-handling code is often scattered across different procedures and files making it difficult to mine error-handling specifications through manual inspection of source code. In this paper, we present a novel framework for mining API error-handling specifications automatically from API client code, without any user input. In our framework, we adapt a trace generation technique to distinguish and generate static traces representing different API run-time behaviors. We apply data mining techniques on the static traces to mine specifications that define correct handling of API errors. We then use the mined specifications to detect API error-handling violations. Our framework mines 62 error-handling specifications and detects 264 real error-handling defects from the analyzed open source packages.