Cloth-Changing Person Re-Identification (CC-ReID) aiming to tackle with person re-identification in the cloth-changing scenario is a realistic but challenging task. Considerable work has been witnessed in recent years. Although these methods achieve good performance, they may require complex disentanglement strategies or extra biological cues. Despite this, due to the limit of clothing diversity, some methods may lead to unreasonable clothes generation and semantic information may be inevitably destroyed. To enrich clothing style diversity in a simple but efficient way and promote the learning of identity-relevant knowledge, we propose a novel Style Mixture and Identity-aware Knowledge Transfer Network (SMI-Net) for cloth-changing person re-identification. Specifically, Style Mixture Module, which mixes statistics of multiple features and generates new clothing style without explicit image generation, is devised to enhance style diversity of clothing. To facilitate clothing-irrelevant knowledge transfer at the low image level, we design a Low-level Semantic Alignment Module to capture fine-grained multi-scale features and calculate low-level semantic alignment loss. Furthermore, High-level Semantic Alignment Loss is presented to assist identity-related knowledge transfer at the high semantic level. Extensive experiments on LTCC and PRCC dataset indicate that our SMI-Net outperforms existing state-of-the-art methods.