Graph Neural Networks (GNNs) have gained considerable prominence in semi-supervised learning tasks in processing graph-structured data, primarily owing to their message-passing mechanism, which largely relies on the availability of clean labels. However, in real-world scenarios, labels on nodes of graphs are inevitably noisy and sparsely labeled, significantly degrading the performance of GNNs. Exploring robust GNNs for semi-supervised node classification in the presence of noisy and sparse labels remains a critical challenge. Therefore, we propose a novel \textbf{G}raph \textbf{N}eural \textbf{N}etwork with \textbf{C}oarse- and \textbf{F}ine-\textbf{G}rained \textbf{D}ivision for mitigating label sparsity and noise, namely GNN-CFGD. The key idea of GNN-CFGD is reducing the negative impact of noisy labels via coarse- and fine-grained division, along with graph reconstruction. Specifically, we first investigate the effectiveness of linking unlabeled nodes to cleanly labeled nodes, demonstrating that this approach is more effective in combating labeling noise than linking to potentially noisy labeled nodes. Based on this observation, we introduce a Gaussian Mixture Model (GMM) based on the memory effect to perform a coarse-grained division of the given labels into clean and noisy labels. Next, we propose a clean labels oriented link that connects unlabeled nodes to cleanly labeled nodes, aimed at mitigating label sparsity and promoting supervision propagation. Furthermore, to provide refined supervision for noisy labeled nodes and additional supervision for unlabeled nodes, we fine-grain the noisy labeled and unlabeled nodes into two candidate sets based on confidence, respectively. Extensive experiments on various datasets demonstrate the superior effectiveness and robustness of GNN-CFGD.