Formal specifications are essential but usually unavailable in software systems. Furthermore, writing these specifications is costly and requires skills from developers. Recently, many automated techniques have been proposed to mine specifications in various formats including finite-state automaton (FSA). However, more works in specification mining are needed to further improve the accuracy of the inferred specifications. In this work, we propose Deep Specification Miner (DSM), a new approach that performs deep learning for mining FSA-based specifications. Our proposed approach uses test case generation to generate a richer set of execution traces for training a Recurrent Neural Network Based Language Model (RNNLM). From these execution traces, we construct a Prefix Tree Acceptor (PTA) and use the learned RNNLM to extract many features. These features are subsequently utilized by clustering algorithms to merge similar automata states in the PTA for constructing a number of FSAs. Then, our approach performs a model selection heuristic to estimate F-measure of FSAs and returns the one with the highest estimated Fmeasure. We execute DSM to mine specifications of 11 target library classes. Our empirical analysis shows that DSM achieves an average F-measure of 71.97%, outperforming the best performing baseline by 28.22%. We also demonstrate the value of DSM in sandboxing Android apps.