The unprecedented capture and application of face images raise increasing concerns on anonymization to fight against privacy disclosure. Most existing methods may suffer from the problem of excessive change of the identity-independent information or insufficient identity protection. In this paper, we present a new face anonymization approach by distracting the intrinsic and extrinsic identity attentions. On the one hand, we anonymize the identity information in the feature space by distracting the intrinsic identity attention. On the other, we anonymize the visual clues (i.e. appearance and geometry structure) by distracting the extrinsic identity attention. Our approach allows for flexible and intuitive manipulation of face appearance and geometry structure to produce diverse results, and it can also be used to instruct users to perform personalized anonymization. We conduct extensive experiments on multiple datasets and demonstrate that our approach outperforms state-of-the-art methods.