Person Re-identification (ReID) aims to retrieve the pedestrian with the same identity across different views. Existing studies mainly focus on improving accuracy, while ignoring their efficiency. Recently, several hash based methods have been proposed. Despite their improvement in efficiency, there still exists an unacceptable gap in accuracy between these methods and real-valued ones. Besides, few attempts have been made to simultaneously explicitly reduce redundancy and improve discrimination of hash codes, especially for short ones. Integrating Mutual learning may be a possible solution to reach this goal. However, it fails to utilize the complementary effect of teacher and student models. Additionally, it will degrade the performance of teacher models by treating two models equally. To address these issues, we propose a salience-guided iterative asymmetric mutual hashing (SIAMH) to achieve high-quality hash code generation and fast feature extraction. Specifically, a salience-guided self-distillation branch (SSB) is proposed to enable SIAMH to generate hash codes based on salience regions, thus explicitly reducing the redundancy between codes. Moreover, a novel iterative asymmetric mutual training strategy (IAMT) is proposed to alleviate drawbacks of common mutual learning, which can continuously refine the discriminative regions for SSB and extract regularized dark knowledge for two models as well. Extensive experiment results on five widely used datasets demonstrate the superiority of the proposed method in efficiency and accuracy when compared with existing state-of-the-art hashing and real-valued approaches. The code is released at https://github.com/Vill-Lab/SIAMH.