The application of machine learning (ML) libraries has been tremendously increased in many domains, including autonomous driving systems, medical, and critical industries. Vulnerabilities of such libraries result in irreparable consequences. However, the characteristics of software security vulnerabilities have not been well studied. In this paper, to bridge this gap, we take the first step towards characterizing and understanding the security vulnerabilities of five well-known ML libraries, including Tensorflow, PyTorch, Sickit-learn, Pandas, and Numpy. To do so, in total, we collected 596 security-related commits to exploring five major factors: 1) vulnerability types, 2) root causes, 3) symptoms, 4) fixing patterns, and 5) fixing efforts of security vulnerabilities in ML libraries. The findings of this study can assist developers in having a better understanding of software security vulnerabilities across different ML libraries and gain a better insight into their weaknesses of them. To make our finding actionable, we further developed DeepMut, an automated mutation testing tool, as a proof-of-concept application of our findings. DeepMut is designed to assess the adequacy of existing test suites of ML libraries against security-aware mutation operators extracted from the vulnerabilities studied in this work. We applied DeepMut on the Tensorflow kernel module and found more than 1k alive mutants not considered by the existing test suits. The results demonstrate the usefulness of our findings.