We present Deep Mesh Denoising Network (DMD-Net), an end-to-end deep learning framework, for solving the mesh denoising problem. DMD-Net consists of a Graph Convolutional Neural Network in which aggregation is performed in both the primal as well as the dual graph. This is realized in the form of an asymmetric two-stream network, which contains a primal-dual fusion block that enables communication between the primal-stream and the dual-stream. We develop a Feature Guided Transformer (FGT) paradigm, which consists of a feature extractor, a transformer, and a denoiser. The feature extractor estimates the local features, that guide the transformer to compute a transformation, which is applied to the noisy input mesh to obtain a useful intermediate representation. This is further processed by the denoiser to obtain the denoised mesh. Our network is trained on a large scale dataset of 3D objects. We perform exhaustive ablation studies to demonstrate that each component in our network is essential for obtaining the best performance. We show that our method obtains competitive or better results when compared with the state-of-the-art mesh denoising algorithms. We demonstrate that our method is robust to various kinds of noise. We observe that even in the presence of extremely high noise, our method achieves excellent performance.