Spectral clustering is a leading clustering method. Two of its major shortcomings are the disjoint optimization process and the limited representation capacity. To address these issues, we propose a deepspectral clustering model (named BootSC), which jointly learns all stages of spectral clustering—affinity matrix construction, spectral embedding, and $k$-means clustering—using a single network in an end-to-end manner. BootSC leverages effective and efficient optimal-transport-derived supervision to bootstrap the affinity matrix and the cluster assignment matrix. Moreover, a semantically-consistent orthogonal re-parameterization technique is introduced to orthogonalize spectral embeddings, significantly enhancing the discrimination capability. Experimental results indicate that BootSC achieves state-of-the-art clustering performance. For example, it accomplishes a notable 16% NMI improvement over the runner-up method on the challenging ImageNet-Dogs dataset.