Recently, intelligent reflecting surface (IRS)-aided millimeter-wave (mmWave) and terahertz (THz) communications are considered in the wireless community. This paper aims to design a beam-based multiple-access strategy for this new paradigm. Its key idea is to make use of multiple sub-arrays over a hybrid digital-analog array to form independent beams, each of which is steered towards the desired direction to mitigate inter-user interference and suppress unwanted signal reflection. The proposed scheme combines the advantages of both orthogonal multiple access (i.e., no inter-user interference) and non-orthogonal multiple access (i.e., full time-frequency resource use). Consequently, it can substantially boost the system capacity, as verified by Monte-Carlo simulations.