Graph Neural Networks (GNNs) have achieved remarkable accuracy in cognitive tasks such as predictive analytics on graph-structured data. Hence, they have become very popular in diverse real-world applications. However, GNN training with large real-world graph datasets in edge-computing scenarios is both memory- and compute-intensive. Traditional computing platforms such as CPUs and GPUs do not provide the energy efficiency and low latency required in edge intelligence applications due to their limited memory bandwidth. Resistive random-access memory (ReRAM)-based processing-in-memory (PIM) architectures have been proposed as suitable candidates for accelerating AI applications at the edge, including GNN training. However, ReRAM-based PIM architectures suffer from low reliability due to their limited endurance, and low performance when they are used for GNN training in real-world scenarios with large graphs. In this work, we propose a learning-for-data-pruning framework, which leverages a trained Binary Graph Classifier (BGC) to reduce the size of the input data graph by pruning subgraphs early in the training process to accelerate the GNN training process on ReRAM-based architectures. The proposed light-weight BGC model reduces the amount of redundant information in input graph(s) to speed up the overall training process, improves the reliability of the ReRAM-based PIM accelerator, and reduces the overall training cost. This enables fast, energy-efficient, and reliable GNN training on ReRAM-based architectures. Our experimental results demonstrate that using this learning for data pruning framework, we can accelerate GNN training and improve the reliability of ReRAM-based PIM architectures by up to 1.6×, and reduce the overall training cost by 100× compared to state-of-the-art data pruning techniques.