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The ability to tailor the damping factor is essential for spintronic and spin-torque applications. Here, we report an approach to manipulate the damping factor of FeGa/MgO(001) films by oblique deposition. Owing to the defects at the surface or interface in thin films, two-magnon scattering (TMS) acts as a non-Gilbert damping mechanism in magnetization relaxation. In this work, the contribution of TMS was characterized by in-plane angular dependent ferromagnetic resonance. It is demonstrated that the intrinsic Gilbert damping is isotropic and invariant, while the extrinsic mechanism related to TMS is anisotropic and can be tuned by oblique deposition. Furthermore, the two and fourfold TMS related to the uniaxial magnetic anisotropy and magnetocrystalline anisotropy were discussed. Our results open an avenue to manipulate magnetization relaxation in spintronic devices.