A simplified three-dimensional Navier-Stokes (3-D NS) model for two fluids, water and landslide material (mudslide) is presented and validated with standard laboratory experiments. Dubbed TSUNAMI3D (Tsunami Solution Using Navier-Stokes Algorithm with Multiple Interfaces) is applied to a 3-D full-scale landslide scenario in the Gulf of Mexico (GOM), i.e., the East-Breaks underwater landslide. The simplified 3-D NS model is conceived to be computationally efficient for tsunami calculations. The simplification is derived from the large aspect ratio of the tsunami waves (wavelength/wave-height) and the selected computational grid that has a smaller aspect ratio. This allows us to assume a horizontal fluid surface in each individual cell containing the interface (air-water, air-mudslide, and water-mudslide). The tracking of fluid interfaces is based on the Volume of Fluid method and the surfaces are obtained by integrating the fluxes of each individual fluid cell along the water column. In the momentum equation, the pressure term is split into two components, hydrostatic and nonhydrostatic. The internal friction is solved in a simplified manner by adjusting the viscosity coefficient. Despite the simplification to get an efficient solution, the numerical results agree fairly well with standard landslide laboratory experiments required by the National Tsunami Hazard Mitigation Program for tsunami model validation. The numerical effect caused by using a sharp versus a diffusive water-mudslide interface for a full-scale landslide-tsunami scenario is also investigated. Observations from this experiment indicated that choosing a sharp or diffusive interface seems to have no remarkable effect at early stages of the tsunami wave propagation. Last, a large scale 3-D numerical simulation is carried out for the ancient GOM's East-Breaks landslide by using the simplified model to calculate the early stages of the tsunami wave propagation.