Intelligent reflecting surface (IRS) has become a cost-effective solution for constructing a smart and adaptive radio environment. Most previous works on IRS have jointly designed the active and passive precoding based on perfectly or partially known channel state information (CSI). However, in delay-sensitive or high-mobility communications, it is imperative to explore more effective methods for leveraging IRS to enhance communication reliability without the need for any CSI. In this paper, we investigate an innovative IRS-aided multiuser communication system, which integrates an IRS with its aided multi-antenna base station (BS) to simultaneously serve multiple high-mobility users through transmit diversity and multiple low-mobility users through active/passive precoding. In specific, we first reveal that when dynamically tuning the IRS's common phase-shift shared with all reflecting elements, its passive precoding gain to any low-mobility user remains unchanged. Inspired by this property, we utilize the design of common phase-shift at the IRS for achieving transmit diversity to serve high-mobility users, yet without requiring any CSI at the BS. Meanwhile, the active/passive precoding design is incorporated into the IRS-integrated BS to serve low-mobility users (assuming the CSI is known). Then, taking into account the interference among different users, we formulate and solve a joint optimization problem of the IRS's reflect precoding and the BS's transmit precoding, with the aim of minimizing the total transmit power at the BS.