The existence of karst compromises the safety of underground engineering, especially during tunnel excavations. Karst conduits are uncovered through tunnel excavations, which may lead to a water–sand inrush disaster. Taking a vertical karst conduit as an example, the process of water–sand inrush through a karst conduit could be viewed as being similar to the process whereby a water–sand mixture flows through the discharge opening of a storage bin. In this study, based on force analysis of a non-aqueous sand body above a karst conduit, the limiting diameter of the karst conduit under force equilibrium was obtained. Considering the effect of water on aqueous sand bodies, the criterion of water–sand inrush was established. We aimed to study water–sand migration and inrush through vertical karst conduits in order to obtain the distribution of the water pressure near a vertical karst conduit, and to explore the relationship between the conduit size, water pressure, and water–sand flow rate; therefore, a simulated testing system for analyzing water–sand inrush through a vertical karst conduit was developed. When the water pressure in the testing chamber was close to the critical head pressure of the water–sand inrush, the water–sand inrush exhibited a pattern of instability—migration—deposition—stability. When the water pressure in the testing chamber exceeded the critical head pressure, the water–sand flow increased first and then stabilized over time. With the increase in the set values of the water pressure and conduit size, the steady flow of the water–sand mixture increased gradually. When the karst conduit was opened suddenly, the actual water pressure in the testing chamber decreased significantly, due to the water–sand mixture flowing out of the testing chamber and the water supply lagging behind. With the stabilization of the water–sand flow, the actual water pressure gradually tended towards stability, but it was still lower than the initial set water pressure. When the karst conduit was opened, the values of the water pressure monitored by the pore pressure gauges all clearly decreased. With the stabilization of the water–sand flow, the water pressure gradually became stable. With the increase in the distance between the pore pressure sensor and the karst conduit, the water pressure values all increased gradually. These test results are significant for further studies of the formation mechanisms of water–sand inrush through vertical karst conduits.