In order to clarify the flow velocity of various block stones in the slurry discharge pipeline and explore the relationship between pipeline blockage formed by block stone deposition and slurry flow velocity, a slurry hydrodynamic calculation formula is derived based on the basic equations of fluid mechanics. Then, from the perspective of motion mechanics, the force analysis is conducted on the most difficult to discharge state of the stones in the horizontal, oblique upward, oblique downward, and vertical upward pipelines. Last, different shapes and particle sizes of stones are analyzed, the formula for calculating the critical mud velocity difference when the mud flows in the mud channel at different tilt angles reaching force equilibrium is derived; the formula for calculating the critical mud velocity of various block stone deposits are then analyzed and derived; and engineering data for trial calculation are set. Conclusions are drawn as follows: (1) With different sizes, shapes, and densities, the block stones flowes at different angles in the mud discharge pipeline with different differential speeds, flow velocity can be automatically classified, and critical mud velocity of sedimentation are different. (2) The stones with lower density and small volume block have faster movement speed and lower critical mud flow rate for sedimentation. (3) With the same weight and density, the stone of spherical shape have the fastest movement speed and the minimum critical mud flow rate for sedimentation, followed by the square shape; the stones of elongated shape have the slowest movement speed and the maximum critical mud flow rate for sedimentation; and the stones with larger length-diameter ratio have the slower flow rate and the greater the critical mud flow rate for sedimentation. (4) A stone has the fastest flow velocity and the lowest critical mud flow velocity in the downward pipeline, followed by that in the horizontal pipeline, and that in the vertical upward pipeline has the lowest flow velocity and the highest critical mud flow velocity. It is important to control the mud flow rate in the launching shaft or in the vertical upward pipeline on the ground. In order to apply an economical mud flow rate for preventing block up in the mud discharge pipeline, the mud flow rate must been calculated.