Metasurfaces have demonstrated numerous functions, including guided scattering and localization of electromagnetic waves, and they are a promising platform for replacing bulk components in the Terahertz frequency regime. In particular, gradient metasurfaces with spatially varying phase responses are a key tool for controlling of electromagnetic wave propagation and scattering phenomena. The generalized Snell’s law is a well-known design principle for the gradient metasurfaces. However, most existing gradient or inhomogeneous metasurfaces suffer from the full phase coverage and deeply subwavelength unit cell dimension, hampering the control over wavefront and the avoidance of unwanted scattering. In a single resonant metasurface, the shift of the phase response is limited for the limited parametric tuning range. Thus, achieving full phase coverage is difficult with a single resonant structure. Furthermore, the application area of the inhomogeneous metasurfaces is constrained due to their low subwavelength profile, which is required for the manipulation of complex wave. Therefore, obtaining the complete phase coverage with a highly subwavelength metasurface unit remains a challenge, in which inhomogeneous metasurfaces can be designed by introducing auxiliary waves in the surface impedance approach. In the first work, a multiresonant deeply subwavelength unit cell with complete phase coverage is developed to numerically demonstrate a high efficiency Terahertz gradient metasurface. In this case, almost all the spurious diffraction are suppressed successfully even with higher number of Floquet modes at lower reflection angles, while preserving good conversion efficiency. The generalized Snell’s law has certain drawbacks beyond its outstanding advantages, which can be overcome through surface impedance approach. However, the metasurfaces based on this approach may violate the local power conservation principle. Incorporating auxiliary waves in the surface impedance approach is a way to address the lacking of power conservation. Nevertheless, most metasurfaces accomplish their functionalities through only a single beam scattering. Beam splitting into multiple diffraction orders can offer an extra freedom in the metasurface. In the second work, an impedance-based design recipe is proposed for beam splitting into multiple diffraction orders, developing an inhomogeneous metasurface by exploiting auxiliary waves. Moreover, a realistic design for the metasurface is studied numerically.