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Feature embeddings are one of the most essential steps when training deep learning based Click-Through Rate prediction models, which map high-dimensional sparse features to dense embedding vectors. Classic human-crafted embedding size selection methods are shown to be "sub-optimal" in terms of the trade-off between memory usage and model capacity. The trending methods in Neural Architecture Search (NAS) have demonstrated their efficiency to search for embedding sizes. However, most existing NAS-based works suffer from expensive computational costs, the curse of dimensionality of the search space, and the discrepancy between continuous search space and discrete candidate space. Other works that prune embeddings in an unstructured manner fail to reduce the computational costs explicitly. In this paper, to address those limitations, we propose a novel strategy that searches for the optimal mixed-dimension embedding scheme by structurally pruning a super-net via Hard Auxiliary Mask. Our method aims to directly search candidate models in the discrete space using a simple and efficient gradient-based method. Furthermore, we introduce orthogonal regularity on embedding tables to reduce correlations within embedding columns and enhance representation capacity. Extensive experiments demonstrate it can effectively remove redundant embedding dimensions without great performance loss.