This paper establishes an efficient model for simulating wave propagation in a multi-layered transversely isotropic (TI) saturated medium. The complex frequency shifted perfectly matched layer (CFSPML) is integrated into the thin layer method (TLM) framework to address instability issues associated with the classical PML in TI media. The three-dimensional closed-form fundamental solution for dynamic sources acting on a layered TI halfspace is derived in the frequency-space domain. By eliminating the necessity of double discrete Fourier transform of spatial coordinates, this approach provides an efficient and accurate tool for exploring wave propagation in saturated soils. Numerical examples are conducted to determine the parameters involved in CFSPML for an unbounded TI saturated medium across various material anisotropy ratios, including the total thickness of CFSPML domain HPML, the parameter Delta gamma related to the number of CFSPML elements, and the reflection coefficient within the discrete CFSPML domain R0. A comprehensive investigation systematically analyses the effect of material anisotropy on dynamic responses. Numerical studies highlight that the anisotropy in the shear modulus exerts the most substantial influence on the dynamic response, followed by Young's modulus and the permeability coefficient. The effect of permeability coefficient anisotropy cannot be disregarded, particularly in the context of fluid sources.