Graph Neural Networks (GNNs) are emerging as a formidable tool for processing non-euclidean data across various domains, ranging from social network analysis to bioinformatics. Despite their effectiveness, their adoption has not been pervasive because of scalability challenges associated with large-scale graph datasets, particularly when leveraging message passing. To tackle these challenges, we introduce NeuraChip, a novel GNN spatial accelerator based on Gustavson's algorithm. NeuraChip decouples the multiplication and addition computations in sparse matrix multiplication. This separation allows for independent exploitation of their unique data dependencies, facilitating efficient resource allocation. We introduce a rolling eviction strategy to mitigate data idling in on-chip memory as well as address the prevalent issue of memory bloat in sparse graph computations. Furthermore, the compute resource load balancing is achieved through a dynamic reseeding hash-based mapping, ensuring uniform utilization of computing resources agnostic of sparsity patterns. Finally, we present NeuraSim, an open-source, cycle-accurate, multi-threaded, modular simulator for comprehensive performance analysis. Overall, NeuraChip presents a significant improvement, yielding an average speedup of 22.1x over Intel's MKL, 17.1x over NVIDIA's cuSPARSE, 16.7x over AMD's hipSPARSE, and 1.5x over prior state-of-the-art SpGEMM accelerator and 1.3x over GNN accelerator. The source code for our open-sourced simulator and performance visualizer is publicly accessible on GitHub https://neurachip.us