Yield stress of thickened tailings is a basic parameter in the design of tailings pipeline transport and discharge systems. To accurately determine the yield stress of thickened tailings, it is essential to develop a rapid determination method suitable for engineering applications and explore the relationship among various factors. In this paper, a high-precision velocity-controlled slump test system was designed to investigate the effects of thickened tailings temperature, lifting speed, slump cylinder shape, and tailings slurry mass concentration on the slump value. The test results indicate that the slump value decreases with the increases in thickened tailings temperature, resulting in a higher yield stress. Lifting speed significantly affects the yield stress, a faster lifting speed produces a larger slump value, which in turn leads to a smaller calculated yield stress. The lifting speed of 0.01 m/s provides a yield stress calculation that is close to the actual value. Moreover, among the tested slump cylinder shapes, the results obtained from the cylinder with dimensions of 100 mm (height) × 100 mm (diameter) are the closest to the actual values. These findings offer technical support for rapid and accurate on-site testing of the rheological parameters of thickened tailings and provide theoretical support for developing disposal methods for tailings.