Hyperspectral imagery (HSI) is widely used in remote sensing for target classification; however, its accurate classification remains challenging due to the scarcity of labeled data. Graph Neural Networks (GNNs) have emerged as a popular method for semi-supervised classification, attracting significant interest in the context of HSI analysis. Nevertheless, conventional GNN-based approaches often rely on a single graph filter to extract HSI characteristics, failing to fully exploit the potential benefits of different graph filters. Additionally, oversmoothing issues plague classical GNNs, further affecting classification performance. To address these drawbacks, we propose a novel approach called Spectral and Autoregressive Moving Average Graph Filter for the Multi-Graph Neural Network (SAM-GNN). This approach leverages two distinct graph filters: one specialized in extracting the spectral characteristics of nodes and the other effectively suppressing graph distortion. Through extensive evaluations, we compare the performance of SAM-GNN with other state-of-the-art methods, employing metrics such as overall accuracy (OA), individual class accuracy (IA), and Kappa coefficient (KC). The results shows that the SAM-GNN provides an improvement in KC, IA, and OA of 6.71%, 5.7%, and 3.93% for the Pavia University dataset and 4.67%, 3.67%, and 3.49% for the Cuprite dataset respectively. Furthermore, we implement SAM-GNN on the Virtex-7 field-programmable gate array (FPGA), demonstrating that the method achieves highly accurate target localization results, bringing us closer to real-world applications in HSI classification.