A finite difference lattice Boltzmann method (FDLBM) for the simulation of mud and debris flows for one-dimensional cases has been introduced. The proposed FDLBM recovers the generalized equations of mud and debris flows, that is, an unsteady one-dimensional Saint-Venant equation, including the effects of the non-Newtonian behavior of the mixture of water and soil, contraction–expansion losses (or large eddy loss), wind force, various geometries, and lateral inflow or outflow. The proposed FDLBM can be implemented for various non-Newtonian viscoplastic constitutive models of the studied mud and debris flows. The method is validated against previous studies for several benchmark cases, including steady-state problems, hydraulic jump tests, dam breaks with dry and wet beds, and slope dam break floods. Finally, the Anhui debris dam failure flood was investigated by this approach, and the results demonstrated a good agreement with the observed computational and field tests.