Cortical cataract, a common type of cataract, is particularly difficult to be diagnosed automatically due to the complex features of the lesions. Recently, many methods based on edge detection or deep learning were proposed for automatic cataract grading. However, these methods suffer a large performance drop in cortical cataract grading due to the more complex cortical opacities and uncertain data. In this paper, we propose a novel Transformer-based Knowledge Distillation Network, called TKD-Net, for cortical cataract grading. To tackle the complex opacity problem, we first devise a zone decomposition strategy to extract more refined features and introduce special sub-scores to consider critical factors of clinical cortical opacity assessment (location, area, density) for comprehensive quantification. Next, we develop a multi-modal mix-attention Transformer to efficiently fuse sub-scores and image modality for complex feature learning. However, obtaining the sub-score modality is a challenge in the clinic, which could cause the modality missing problem instead. To simultaneously alleviate the issues of modality missing and uncertain data, we further design a Transformer-based knowledge distillation method, which uses a teacher model with perfect data to guide a student model with modality-missing and uncertain data. We conduct extensive experiments on a dataset of commonly-used slit-lamp images annotated by the LOCS III grading system to demonstrate that our TKD-Net outperforms state-of-the-art methods, as well as the effectiveness of its key components. Codes are available at https://github.com/wjh892521292/Cataract_TKD-Net.