Title: GARNET: A Spectral Approach to Robust and Scalable Graph Neural Networks. Abstract: Graph neural networks (GNNs) have been increasingly deployed in various applications that involve learning on non-Euclidean data. However, recent studies show that GNNs are vulnerable to graph adversarial attacks. Although there are several defense methods to improve GNN adversarial robustness, they fail to perform well on low homophily graphs. In addition, few of those defense models can scale to large graphs due to their high computational complexity and memory usage. In this paper, we propose GARNET, a scalable spectral method to boost the adversarial robustness of  GNN models for both homophilic and heterophilic graphs. GARNET first computes a reduced-rank yet sparse approximation of the adversarial graph by exploiting an efficient spectral graph embedding and sparsification scheme. Next, GARNET trains an adaptive graph filter on the reduced-rank graph for node representation refinement, which is subsequently leveraged to guide label propagation for further enhancing the quality of node embeddings. GARNET has been evaluated on both homophilic and heterophilic datasets, including a large graph with millions of nodes. Our extensive experiment results show that GARNET increases adversarial accuracy over state-of-the-art GNN (defense) models by up to $9.96\%$ and $15.17\%$ on homophilic and heterophilic graphs, respectively.