The recent rapid advancements in both sensing and machine learning technologies have given rise to the universal collection and utilization of people's biometrics, such as fingerprints, voices, retina/facial scans, or gait/motion/gestures data, enabling a wide range of applications including authentication, health monitoring, or much more sophisticated analytics. While providing better user experiences and deeper business insights, the use of biometrics has raised serious privacy concerns due to their intrinsic sensitive nature and the accompanying high risk of leaking sensitive information such as identity or medical conditions. In this paper, we propose a novel modality-agnostic data transformation framework that is capable of anonymizing biometric data by suppressing its sensitive attributes and retaining features relevant to downstream machine learning-based analyses that are of research and business values. We carried out a thorough experimental evaluation using publicly available facial, voice, and motion datasets. Results show that our proposed framework can achieve a \highlight{high suppression level for sensitive information}, while at the same time retain underlying data utility such that subsequent analyses on the anonymized biometric data could still be carried out to yield satisfactory accuracy.