Even pruned by the state-of-the-art network compression methods, recent research shows that deep learning model training still suffers from the demand of massive data usage. In particular, Graph Neural Networks (GNNs) training upon such non-Euclidean graph data often encounters relatively higher time costs, due to its irregular and nasty density properties, compared with data in the regular Euclidean space (e.g., image or text). Another natural property concomitantly with graph is class-imbalance which cannot be alleviated by the massive graph data while hindering GNNs' generalization. To fully tackle these unpleasant properties, (i) theoretically, we introduce a hypothesis about what extent a subset of the training data can approximate the full dataset's learning effectiveness. The effectiveness is further guaranteed and proved by the gradients' distance between the subset and the full set; (ii) empirically, we discover that during the learning process of a GNN, some samples in the training dataset are informative for providing gradients to update model parameters. Moreover, the informative subset is not fixed during training process. Samples that are informative in the current training epoch may not be so in the next one. We refer to this observation as dynamic data sparsity. We also notice that sparse subnets pruned from a well-trained GNN sometimes forget the information provided by the informative subset, reflected in their poor performances upon the subset. Based on these findings, we develop a unified data-model dynamic sparsity framework named Graph Decantation (GraphDec) to address challenges brought by training upon a massive class-imbalanced graph data. The key idea of GraphDec is to identify the informative subset dynamically during the training process by adopting sparse graph contrastive learning. Extensive experiments on multiple benchmark datasets demonstrate that GraphDec outperforms state-of-the-art baselines for class-imbalanced graph classification and class-imbalanced node classification tasks, with respect to classification accuracy and data usage efficiency.