Vital sign monitoring plays a critical role in tracking the physiological state of people and enabling various health-related applications (e.g., recommending a change of lifestyle, examining the risk of diseases). Traditional approaches rely on hospitalization or body-attached instruments, which are costly and intrusive. Therefore, researchers have been exploring contact-less vital sign monitoring with radio frequency signals in recent years. Early studies with continuous wave radars/WiFi devices work on detecting vital signs of a single individual, but it still remains challenging to simultaneously monitor vital signs of multiple subjects, especially those who locate in proximity. In this paper, we design and implement a time-division multiplexing (TDM) phased-MIMO radar sensing scheme for high-precision vital sign monitoring of multiple people. Our phased-MIMO radar can steer the mmWave beam towards different directions with a micro-second delay, which enables capturing the vital signs of multiple individuals at the same radial distance to the radar. Furthermore, we develop a TDM-MIMO technique to fully utilize all transmitting antenna (TX)-receiving antenna (RX) pairs, thereby significantly boosting the signal-to-noise ratio. Based on the designed TDM phased-MIMO radar, we develop a system to automatically localize multiple human subjects and estimate their vital signs. Extensive evaluations show that under two-subject scenarios, our system can achieve an error of less than 1 beat per minute (BPM) and 3 BPM for breathing rate (BR) and heartbeat rate (HR) estimations, respectively, at a subject-to-radar distance of $1.6~m$. The minimal subject-to-subject angle separation is $40°$, corresponding to a close distance of $0.5~m$ between two subjects, which outperforms the state-of-the-art.