The aim of this study was to evaluate the effect of β-tricalcium phosphate (β-TCP) modification on the structural, mechanical, thermal, and functional properties of a shape-memory terpolymer, with a focus on its potential application in 4D printing technology and medical implant production. The integration of β-TCP into the filament matrix and scaffolds was confirmed through microscopic (SEM, stereoscopic) and spectroscopic (FTIR, EDS) analyses. FTIR spectra indicated successful incorporation of β-TCP into the polymer. Differential scanning calorimetry (DSC) analysis revealed a shift toward a more amorphous structure following β-TCP modification, improving processing properties, particularly for 3D printing. Thermal stability was enhanced, as β-TCP delayed depolymerization of the polymer matrix. Shape-memory studies demonstrated effective recovery in both modified and unmodified samples, although β-TCP slightly reduced recovery performance. In vitro cell culture studies showed that β-TCP-modified terpolymer significantly increased cell viability and alkaline phosphatase (ALP) activity after 3 weeks. The β-TCP-modified terpolymer can be tailored for applications where partial shape recovery is acceptable, such as bone scaffolds or implants designed to promote osteointegration.