The underwater acoustic signals separation is a key technique for the underwater communications. The existing methods are mostly model-based, and could not accurately characterise the practical underwater acoustic communication environment. They are only suitable for binary signal separation, but cannot handle multivariate signal separation. On the other hand, the recurrent neural network (RNN) shows powerful capability in extracting the features of the temporal sequences. Inspired by this, in this paper, we present a data-driven approach for underwater acoustic signals separation using deep learning technology. We use the Bi-directional Long Short-Term Memory (Bi-LSTM) to explore the features of Time-Frequency (T-F) mask, and propose a T-F mask aware Bi-LSTM for signal separation. Taking advantage of the sparseness of the T-F image, the designed Bi-LSTM network is able to extract the discriminative features for separation, which further improves the separation performance. In particular, this method breaks through the limitations of the existing methods, not only achieves good results in multivariate separation, but also effectively separates signals when mixed with 40dB Gaussian noise signals. The experimental results show that this method can achieve a $97\%$ guarantee ratio (PSR), and the average similarity coefficient of the multivariate signal separation is stable above 0.8 under high noise conditions.