Graph neural networks (GNNs) have a powerful ability to capture long-range spatial correlations in hyperspectral images (HSIs). However, existing GNN-based HSI classification methods are vulnerable to hand-crafted graphs, as the manner in which these graphs are constructed are often inappropriate and are likely to violate intrinsic graph properties, such as sparsity and low-rank. More importantly, the goal of HSI classification is to categorize each individual pixel into a land-cover class, but existing methods usually overuse global dependencies and ignore the importance of individualized spectral characteristics. Therefore, this paper proposes a Global-to-Local decoupling Graph network (GoLoG) to conduct HSI classification in a global-to-local framework, which jointly optimizes the graph structure and network parameters guided by both intrinsic graph properties and classification loss. Specifically, a novel global-to-local network framework with successive global and local graph convolutional stages is constructed. By decoupling global and local stages, global contextual information can be exploited, and the individualized information of each hyperspectral pixel can be emphasized for HSI classification. Second, a sparse and low-rank graph structure learning model is proposed to refine and renovate the initial-construct graph. Finally, to unify graph structure learning and network training, a joint alternating update algorithm is introduced to jointly optimize the sparse and low-rank graph structure learning model and the global-to-local network framework. Extensive experiments demonstrate that the proposed GoLoG has obvious advantages compared with other state-of-the-art HSI classification methods.