Analog/digital hybrid beamforming architectures with large-scale antenna arrays have been widely considered in millimeter wave (mmWave) communication systems because they can address the tradeoff between performance and hardware efficiency compared with traditional fully-digital beamforming. Most of the prior work on hybrid beamforming focused on fullyconnected architecture or partially-connected scheme with fixedsubarrays, in which the analog beamformers are usually realized by infinite-resolution phase shifters (PSs). In this paper, we introduce a novel hybrid beamforming architecture with dynamic subarrays and hardware-efficient low-resolution PSs for mmWave multiuser multiple-input single-output (MU-MISO) systems. By dynamically connecting each RF chain to a non-overlap subarray via a switch network and PSs, we can exploit multiple-antenna and multiuser diversities to mitigate the performance loss due to the use of practical low-resolution PSs. An iterative hybrid beamformer design algorithm is first proposed based on fractional programming (FP), aiming at maximizing the sum-rate performance of the MU-MISO system. In an effort to reduce the complexity, we also present a simple heuristic hybrid beamformer design algorithm for the dynamic subarray scheme. Extensive simulation results demonstrate the advantages of the proposed hybrid beamforming architecture with dynamic subarrays and low-resolution PSs compared to existing fixed-subarray schemes.