Spectral clustering plays a significant role in applications that rely on multi-view data due to its well-defined mathematical framework and excellent performance on arbitrarily-shaped clusters. Unfortunately, directly optimizing the spectral clustering inevitably results in an NP-hard problem due to the discrete constraints on the clustering labels. Hence, conventional approaches intuitively include a relax-and-discretize strategy to approximate the original solution. However, there are no principles in this strategy that prevent the possibility of information loss between each stage of the process. This uncertainty is aggravated when a procedure of heterogeneous features fusion has to be included in multi-view spectral clustering. In this paper, we avoid an NP-hard optimization problem and develop a general framework for multi-view discrete graph clustering by directly learning a consensus partition across multiple views, instead of using the relax-and-discretize strategy. An effective re-weighting optimization algorithm is exploited to solve the proposed challenging problem. Further, we provide a theoretical analysis of the model's convergence properties and computational complexity for the proposed algorithm. Extensive experiments on several benchmark datasets verify the effectiveness and superiority of the proposed algorithm on clustering and image segmentation tasks.