Recent developed deep unsupervised methods allow us to jointly learn representation and cluster unlabelled data. These deep clustering methods mainly focus on the correlation among samples, e.g., selecting high precision pairs to gradually tune the feature representation, which neglects other useful correlations. In this paper, we propose a novel clustering framework, named deep comprehensive correlation mining (DCCM), for exploring and taking full advantage of various kinds of correlations behind the unlabeled data from three aspects: 1) Instead of only using pairwise information, pseudo-label supervision is proposed to investigate category information and learn discriminative features. 2) The features’ robustness to image transformation of input space is fully explored, which benefits the network learning and significantly improves the performance. 3) The triplet mutual information among features is presented for clustering problem to lift the recently discovered instance-level deep mutual information to a triplet-level formation, which further helps to learn more discriminative features. Extensive experiments on several challenging datasets show that our method achieves good performance, e.g., attaining 62.3% clustering accuracy on CIFAR-10, which is 10.1% higher than the state-of-the-art result.