In this work, the ternary titanium, copper, and silver (Ti-Cu-Ag) system is investigated as a potential candidate for the production of mechanically robust biomedical thin films. The coatings are produced by physical vapor deposition—magnetron sputtering (MS-PVD). The composite thin films are deposited on a silicon (100) substrate. The ratio between Ti and Cu was approximately kept one, with the variation of the Ag content between 10 and 35 at.%, while the power on the targets is changed during each deposition to get the desired Ag content. Thin film characterization is performed by X-ray diffraction (XRD), nanoindentation (modulus and hardness), to quantitatively evaluate the scratch adhesion, and atomic force microscopy to determine the surface topography. The residual stresses are measured by focused ion beam and digital image correlation method (FIB-DIC). The produced Ti-Cu-Ag thin films appear to be smooth, uniformly thick, and exhibit amorphous structure for the Ag contents lower than 25 at.%, with a transition to partially crystalline structure for higher Ag concentrations. The Ti-Cu control film shows higher values of 124.5 GPa and 7.85 GPa for modulus and hardness, respectively. There is a clear trend of continuous decrease in the modulus and hardness with the increase of Ag content, as lowest value of 105.5 GPa and 6 GPa for 35 at.% Ag containing thin films. In particular, a transition from the compressive (−36.5 MPa) to tensile residual stresses between 229 MPa and 288 MPa are observed with an increasing Ag content. The obtained results suggest that the Ag concentration should not exceed 25 at.%, in order to avoid an excessive reduction of the modulus and hardness with maintaining (at the same time) the potential for an increase of the antibacterial properties. In summary, Ti-Cu-Ag thin films shows characteristic mechanical properties that can be used to improve the properties of biomedical implants such as Ti-alloys and stainless steel.