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Due to its effectivity and efficiency, deep hashing approaches are widely used for large-scale visual search. However, it is still challenging to produce compact and discriminative hash codes for images associated with multiple semantics for two main reasons, 1) similarity constraints designed in most of the existing methods are based upon an oversimplified similarity assignment(i.e., 0 for instance pairs sharing no label, 1 for instance pairs sharing at least 1 label), 2) the exploration in multi-semantic relevance are insufficient or even neglected in many of the existing methods. These problems significantly limit the discrimination of generated hash codes. In this paper, we propose a novel self-supervised asymmetric deep hashing method with a margin-scalable constraint(SADH) approach to cope with these problems. SADH implements a self-supervised network to sufficiently preserve semantic information in a semantic feature dictionary and a semantic code dictionary for the semantics of the given dataset, which efficiently and precisely guides a feature learning network to preserve multilabel semantic information using an asymmetric learning strategy. By further exploiting semantic dictionaries, a new margin-scalable constraint is employed for both precise similarity searching and robust hash code generation. Extensive empirical research on four popular benchmarks validates the proposed method and shows it outperforms several state-of-the-art approaches.