Time-dependent viscosity characteristics of quick-setting slurry grouting lead to uneven distribution of viscosity in the slurry diffusion zone. At present, there still lacks reasonable and effective slurry-water interaction analysis method to reveal the diffusion behavior of quick-setting slurry in dynamic water of karst fractures and conduits. A Sequential Flow and Solidification (SFS) method was proposed, taking the spatial-temporal evolution of slurry viscosity into account. In addition, the validity and necessity of the SFS method were verified. Based on the SFS method, the slurry diffusion process under different flow velocities in a fracture was analyzed and the effects of flow velocities on the changes of the grouting pressure, the counter-flow diffusion distance, and the down-flow diffusion behavior were explored. The applicability and the feasibility of studying the slurry diffusion mechanism in a wide-open fracture on an engineering scale were determined. The SFS method is also applied to the numerical investigation of dynamic grouting and blocking of flowing water in karst conduits. It achieves the visualization of dynamic grouting in the conduit, and explores a reasonable and effective method for dynamic grouting via the flow control technology. The outlet flow, the loss rate of slurry, the distribution laws of velocity and pressure inside the conduit during plugging are furtherly analyzed. In addition, the mechanism of flow control on dynamic grouting and plugging of the large-flow karst conduits is revealed. Moreover, the results were applied to the large-scale water inrush control project of Hejing Limestone Mine, China. The SDS method can be used to simulate the dynamic water grouting process, providing an improved method for the simulation of permeation and compaction grouting.