In the construction of mountain tunnels, biased and water-rich strata are often encountered. During tunnel excavation, the fluid–solid coupling has a great influence on the stability of the surrounding rock. This effect will be more severe when the terrain is biased. The bias tunnel points out the asymmetric load of the rocks which are surrounding the tunnels through the drilling or construction process due to the topographic situation. These loads can cause inverse actions during tunnel construction. Therefore, the effect of fluid–solid coupling on the displacement field, stress field, and seepage field of the tunnel surrounding rock under different biased terrains are studied in this paper. In the context of the Youzishu tunnel project, the numerical model is established to define the degree of terrain bias. Besides, the concept of bias coefficient is introduced. To achieve what is needed, 10 sets of increasing bias coefficients are obtained, by changing the inclination of the terrain to study the influence of formation bias degree on tunnel excavation in water-rich formations. After an in-depth analysis of the simulation results, it is found that the influence of fluid–structure interaction cannot be ignored. By analyzing ten groups of data under different working conditions, the biased terrain will aggravate this effect. As far as the displacement field of the surrounding rock is concerned, the biased formation has a greater impact on the deeply buried side than on the shallow-buried side, and has a greater impact on the vault than on the arch bottom. In addition, by analyzing the stress field and seepage field of the surrounding rock, a similar result can be obtained: the influence of formation bias on the deeply buried side is greater than that on the shallow-buried side, and the biased terrain will increase the pore pressure outside the tunnel lining and increase the water inflow. Finally, the locations where the displacement, stress, water pressure, and water inflow are the largest during the tunnel excavation process are found by the simulations and analyzed. Thus, attention can be paid to these locations, permitting a focus on protection during the construction process.