Spectral clustering, a prominent unsupervised machine learning method, involves a critical task of constructing a similarity matrix. In existing approaches, this matrix is either computed once for all or updated alternatively. However, the former struggles to capture comprehensive relationships among data points, and the latter is often impractical for large-scale problems. This study introduces a new clustering framework with self-guidance and a block diagonal representation, retaining valuable information from previous cycles. To our knowledge, this is the first application of such a framework to spectral clustering, with a key distinction being the reclassification of samples in each cycle. To reduce computational overhead, we employ a block diagonal representation with Nyström approximation for constructing the similarity matrix. Theoretical results justify the rationality of approximate computations in spectral clustering. Comprehensive experiments on benchmark datasets demonstrate the superiority of our proposed algorithms over state-of-the-art methods for large-scale clustering. Notably, our framework has the potential to enhance clustering algorithms, performing well even with a randomly chosen initial guess.