Just-in-time (JIT) compilers are key components for many popular programming languages with managed runtimes (e.g., Java and JavaScript). JIT compilers perform optimizations and generate native code at runtime based on dynamic profiling data, to improve the execution performance of the running application. Like other software systems, JIT compilers might have software bugs, and prior work has developed a number of automated techniques for detecting correctness bugs (i.e., generated native code does not semantically match that of the original code). However, no prior work has targeted JIT compiler performance bugs, which can cause significant performance degradation in a running application. These performance bugs are challenging to detect due to the complexity and dynamic nature of JIT compilers. In this paper, we present the first work on demystifying JIT compiler performance bugs. First, we perform an empirical study across four widely used JIT compilers for the Java and JavaScript languages. Our manual analysis of 191 bug reports uncovers common patterns in how performance bugs manifest, their symptoms, and their root causes. Second, informed by these insights, we propose a lightweight technique, which we call tiered differential performance testing, to automatically detect JIT compiler performance bugs. We further introduce practical optimizations such as test prioritization, which reduces testing time by 92.4% without compromising bug-detection capability, and automatic false-positive and duplicate filtering, which substantially reduce manual inspection effort. Our work discovered 12 previously unknown performance bugs in the Oracle HotSpot and Graal JIT compilers, with 11 confirmed or fixed by developers.