In the era of pre-trained models, image clustering task is usually addressed by two relevant stages: a) to produce features from pre-trained vision models; and b) to find clusters from the pre-trained features. However, these two stages are often considered separately or learned by different paradigms, leading to suboptimal clustering performance. In this paper, we propose a unified framework, termed graph Cut-guided Maximal Coding Rate Reduction (CgMCR \(^2\) ), for jointly learning the structured embeddings and the clustering. To be specific, we attempt to integrate an efficient clustering module into the principled framework for learning structured representation, in which the clustering module is used to provide partition information to guide the cluster-wise compression and the learned embeddings is aligned to desired geometric structures in turn to help for yielding more accurate partitions. We conduct extensive experiments on both standard and out-of-domain image datasets and experimental results validate the effectiveness of our approach.