Reconfigurable intelligent surface (RIS) has recently been proposed as a smart reflector that significantly provides an energy and spectrum efficient solution for beyond 5G communications. The RIS is a planar surface made of a large number of reflecting elements. More specifically, an array of phase shifters. RIS provides an additional degree of freedom (DoF) by smartly reconfiguring the wireless environment. However, channel estimation (CE) is a challenging issue to benefit from RIS. To obtain the accurate channel state information (CSI) at the base station (BS), the number of channel coefficients is proportional to the number of reflecting elements and the number of users. Therefore, the training overhead prohibitively increases as the number of reflecting elements and/or users increases. In this paper, we propose a two-stage CE approach in mmWave communications to address this issue. In the first stage, we reduce the number of active users in the training period. Then we exploit the sparsity of the mmWave channel of the active users to divide the estimation process into three simple subproblems. In the second stage, we use the partial CSI collected in the first stage, exploit the spatial-temporal correlation between the channels for nearby users to estimate the channels for the remaining users. We deploy the spatial-temporal-spectral (STS) framework based on deep convolutional neural networks (CNNs) to estimate the channel coefficients for inactive users in the training period. Simulation results demonstrate that the performance of the proposed approach outperforms a benchmark scheme.