Due to the complexity of hyperspectral data and the scarcity of labeled samples, unsupervised clustering segmentation has become a hot spot of interest in remote sensing. Sparse subspace clustering (SSC) is the most common clustering approach at the moment, although its computational cost restricts its use on big remote sensing datasets. Furthermore, SSC’s neglect of spatial information and limited recognition ability hinder the spatial homogeneity of clustering results. Hence, this work proposes a fast spectral clustering algorithm for local cosine similarity graphs. First, the fuzzy simple linear iterative clustering superpixel method is introduced into the SSC framework to treat superpixels as homogeneous entities and obtain global similarity maps using very low computational and spatial overheads. Then, a cosine similarity measure that combines spectral information and spatial information is used to obtain a local similarity graph, which enhances the accuracy of the final classification and suppresses noise. Extensive testing demonstrates the value of the proposed method. Compared to state-of-the-art SSC-based algorithms, it offers superior classification performance, noise immunity, and very little computational overhead.