The discrete element method (DEM) is employed to study the self-diffusion motions and mixing of cohesive powders with the effect of liquid bridges in a two-dimensional vibrated granular bed. The dynamic liquid bridge forces are considered as the cohesive forces between particles, and three types of viscous liquids with different values of viscosity are used. A simplified model of dynamic bridge strength based on the superposition of lubrication and circular approximation is incorporated in the simulation model. It is found that the granular temperatures and the self-diffusion coefficients of cohesive powders are highly anisotropic with a greater component in the vertical direction. The diffusion coefficients for cohesive powders are larger than those of cohesionless powders and are related to the interstitial liquid volume. The mixing is strongly dependent on the self-diffusivity and is related to the magnitude of interstitial liquid volume. The variations of the self-diffusion coefficients and the mixing rate for three types of interstitial liquids show that the mixing rate constants are proportional to the diffusion coefficients.