The rapid growth of audio-centric platforms and applications such as WhatsApp and Twitter has transformed the way people communicate and share audio content in modern society. However, these platforms are increasingly misused to disseminate harmful audio content, such as hate speech, deceptive advertisements, and explicit material, which can have significant negative consequences (e.g., detrimental effects on mental health). In response, researchers and practitioners have been actively developing and deploying audio content moderation tools to tackle this issue. Despite these efforts, malicious actors can bypass moderation systems by making subtle alterations to audio content, such as modifying pitch or inserting noise. Moreover, the effectiveness of modern audio moderation tools against such adversarial inputs remains insufficiently studied. To address these challenges, we propose MTAM, a Metamorphic Testing framework for Audio content Moderation software. Specifically, we conduct a pilot study on 2000 audio clips and define 14 metamorphic relations across two perturbation categories: Audio Features-Based and Heuristic perturbations. MTAM applies these metamorphic relations to toxic audio content to generate test cases that remain harmful while being more likely to evade detection. In our evaluation, we employ MTAM to test five commercial textual content moderation software and an academic model against three kinds of toxic content. The results show that MTAM achieves up to 38.6%, 18.3%, 35.1%, 16.7%, and 51.1% error finding rates (EFR) when testing commercial moderation software provided by Gladia, Assembly AI, Baidu, Nextdata, and Tencent, respectively, and it obtains up to 45.7% EFR when testing the state-of-the-art algorithms from the academy.