The sparse unmixing of hyperspectral data has attracted much attention in recent years because it does not need to estimate the number of endmembers nor consider the lack of pure pixels in a given hyperspectral scene. However, the high mutual coherence of spectral libraries strongly affects the practicality of sparse unmixing. The collaborative sparse unmixing via variable splitting and augmented Lagrangian (CLSUnSAL) algorithm is a classic sparse unmixing algorithm that performs better than other sparse unmixing methods. In this paper, we propose a CLSUnSAL-based hyperspectral unmixing method based on dictionary pruning and reweighted sparse regression. First, the algorithm identifies a subset of the original library elements using a dictionary pruning strategy. Second, we present a weighted sparse regression algorithm based on CLSUnSAL to further enhance the sparsity of endmember spectra in a given library. Third, we apply the weighted sparse regression algorithm on the pruned spectral library. The effectiveness of the proposed algorithm is demonstrated on both simulated and real hyperspectral datasets. For simulated data cubes (DC1, DC2 and DC3), the number of the pruned spectral library elements is reduced by at least 94% and the runtime of the proposed algorithm is less than 10% of that of CLSUnSAL. For simulated DC4 and DC5, the runtime of the proposed algorithm is less than 15% of that of CLSUnSAL. For the real hyperspectral datasets, the pruned spectral library successfully reduces the original dictionary size by 76% and the runtime of the proposed algorithm is 11.21% of that of CLSUnSAL. These experimental results show that our proposed algorithm not only substantially improves the accuracy of unmixing solutions but is also much faster than some other state-of-the-art sparse unmixing algorithms.