Recent years have witnessed wider adoption of Automated Speech Recognition (ASR) techniques in various domains. Consequently, evaluating and enhancing the quality of ASR systems is of great importance. This paper proposes ASDF, an Automated Speech Recognition Differential Testing Framework for testing ASR systems. ASDF extends an existing ASR testing tool, the CrossASR++, which synthesizes test cases from a text corpus. However, CrossASR++ fails to make use of the text corpus efficiently and provides limited information on how the failed test cases can improve ASR systems. To address these limitations, our tool incorporates two novel features: (1) a text transformation module to boost the number of generated test cases and uncover more errors in ASR systems and (2) a phonetic analysis module to identify on which phonemes the ASR system tend to produce errors. ASDF generates more high-quality test cases by applying various text transformation methods (e.g., change tense) to the texts in failed test cases. By doing so, ASDF can utilize a small text corpus to generate a large number of audio test cases, something which CrossASR++ is not capable of. In addition, ASDF implements more metrics to evaluate the performance of ASR systems from multiple perspectives. ASDF performs phonetic analysis on the identified failed test cases to identify the phonemes that ASR systems tend to transcribe incorrectly, providing useful information for developers to improve ASR systems. The demonstration video of our tool is made online at https://www.youtube.com/watch?v=DzVwfc3h9As. The implementation is available at https://github.com/danielyuenhx/asdf-differential-testing.