Graph neural networks (GNNs) have emerged as powerful tools for representation learning. Their efficacy depends on their having an optimal underlying graph. In many cases, the most relevant information comes from specific subgraphs. In this work, we introduce a GNN-based framework (graph-partitioned GNN [GP-GNN]) to partition the GNN graph to focus on the most relevant subgraphs. Our approach jointly learns task-dependent graph partitions and node representations, making it particularly effective when critical features reside within initially unidentified subgraphs. Protein liquid-liquid phase separation (LLPS) is a problem especially well-suited to GP-GNNs because intrinsically disordered regions (IDRs) are known to function as protein subdomains in it, playing a key role in the phase separation process. In this study, we demonstrate how GP-GNN accurately predicts LLPS by partitioning protein graphs into task-relevant subgraphs consistent with known IDRs. Our model achieves state-of-the-art accuracy in predicting LLPS and offers biological insights valuable for downstream investigation.