Knee osteoarthritis (OA) is the most common osteoarthritis and a leading cause of disability. Cartilage defects are regarded as major manifestations of knee OA, which are visible by magnetic resonance imaging (MRI). Thus early detection and assessment for knee cartilage defects are important for protecting patients from knee OA. In this way, many attempts have been made on knee cartilage defect assessment by applying convolutional neural networks (CNNs) to knee MRI. However, the physiologic characteristics of the cartilage may hinder such efforts: the cartilage is a thin curved layer, implying that only a small portion of voxels in knee MRI can contribute to the cartilage defect assessment; heterogeneous scanning protocols further challenge the feasibility of the CNNs in clinical practice; the CNN-based knee cartilage evaluation results lack interpretability. To address these challenges, we model the cartilages structure and appearance from knee MRI into a graph representation, which is capable of handling highly diverse clinical data. Then, guided by the cartilage graph representation, we design a non-Euclidean deep learning network with the self-attention mechanism, to extract cartilage features in the local and global, and to derive the final assessment with a visualized result. Our comprehensive experiments show that the proposed method yields superior performance in knee cartilage defect assessment, plus its convenient 3D visualization for interpretability.