The highly directional beams applied in millimeter wave (mmWave) cellular networks make it possible to achieve near interference-free (NIF) transmission under judiciously designed space-time user scheduling, where the power of intra-/inter-cell interference between any two users is below a predefined threshold. In this paper, we investigate two aspects of the NIF space-time user scheduling in a multi-cell mmWave network with multi-RF-chain base stations. Firstly, given that each user has a requirement on the number of space-time resource elements, we study the NIF user scheduling problem to minimize the unfulfilled user requirements, so that the space-time resources can be utilized most efficiently and meanwhile all strong interferences are avoided. A near-optimal scheduling algorithm is proposed with performance close to the lower bound of unfulfilled requirements. Furthermore, we study the joint NIF user scheduling and power allocation problem to minimize the power consumption under the constraint of rate requirements. Based on our proposed NIF scheduling, an energy-efficient joint scheduling and power allocation scheme is designed with limited channel state information, which outperforms the existing independent set based schemes, and has near-optimal performance as well.