The Greenland Ice Sheet (GrIS) plays an important role in the climate system. Since the twenty-first century, GrIS has been melting rapidly due to oceanic and atmospheric warming, leading to a global mean sea level rise of more than 1 millimeter per year. Since 2002, the total amount of GrIS mass changes can be accurately quantified from gravity anomaly observed by the Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO) satellite missions. GRACE(-FO) missions reveal that the GrIS has lost an average of over 260 billion tonnes of ice every year, but they cannot quantify the detailed spatial distribution of these mass changes due to a limiting spatial resolution of about 300 kilometers. In this study, we develop a deep learning method to downscale the GrIS mass anomaly products to 5-km spatial resolution by benefiting from other data sources, including satellite altimetry measurements and surface mass balance modelling. To consider Greenland's complex coastlines and reduce land-ocean leakages, we convert the gridded products into graphs, which allows us to have more flexible shapes of target areas. We test different variants of graph neural networks (GNNs), including graph convolutional networks (GCNs) and graph attention networks (GATs), to estimate the connections among neighboring locations. The GrIS mass anomalies are decomposed into long-term trends and monthly variations, which are later estimated separately by considering different high-resolution products. For the long-term trends, we use 5-year elevation changes measured by multiple altimetry missions as input to provide high spatial resolution information. The surface mass balance estimations from regional climate models and monthly elevation changes inferred from satellite altimetry are considered on the monthly scale. At the same time, the large-scale averages of downscaled mass anomalies are forced to follow GRACE(-FO) products. Ultimately, the downscaled GrIS mass anomalies agree well with GRACE(-FO) products, with large-scale RMSE of around one centimeter per year, and improved more than 60% compared to the altimetry-only estimations. The high-resolution spatial information of 5 kilometers measured by altimetry missions is successfully retained with an average pixel-wise correlation over 0.96. The downscaled GrIS mass anomaly product is valuable for understanding the spatial distribution of GrIS mass changes and is especially beneficial for analyzing individual glacier systems, which is not possible with current available GrIS mass anomaly products.