To avoid waste from a large section space structure layout and deep burial to improve the structural strength and stability, anchor technology is introduced, and combined with the advantages of the supporting wall, a new debris flow grille dam is proposed. Starting from the force process and damage mechanism of the new debris flow grille dam, the computation formula for the anti-pulling force and the total displacement is given. The anti-pulling force includes the sidewall frictional resistance of the anchor pier and the positive pressure of the front end face of the anchor pier. The total displacement includes three parts: the elastic deformation of the cable, the relative shear displacement between the anchor pier and the surrounding soil, and the compression deformation of the soil at the front of the anchor pier. Finally, the influence of soil parameters and anchor pier size on the anti-pulling force and displacement deformation of the anchor-pulling system is analyzed by examples, and the results are compared with the numerical results. The results show that the displacement deformation decreases gradually with increasing elastic modulus of the soil around the anchor pier and increases with increasing Poisson's ratio. The change in elastic modulus mainly affects the relative shear displacement of the anchor pier and soil and the compressive deformation of the soil at the front end of the anchor pier. Poisson's ratio has the greatest influence on the relative shear displacement of the anchor pier and soil. A larger anchor pier is not better; thus, it is wise to choose the economic design dimension. Theoretical and numerical simulation results are consistent, showing a linear growth trend. The results of this paper can further improve the theoretical calculation method of the new debris flow grille dam, thus making it widely used in more debris flow control projects.