The aim of this paper was to design and fabricate a novel composite scaffold based on the combination of 3D-printed polylactic acid-based triply periodic minimal surfaces (TPMSs) and cell-laden alginate hydrogel. This novel scaffold improves the low mechanical properties of alginate hydrogel and can also provide a scaffold with a suitable pore size, which can be used in bone regeneration applications. In this regard, an implicit function was used to generate some gyroid TPMS scaffolds. Then the fused deposition modeling process was employed to print the scaffolds. Moreover, the micro computed tomography technique was employed to assess the microstructure of 3D-printed TPMS scaffolds and obtain the real geometries of printed scaffolds. The mechanical properties of composite scaffolds were investigated under compression tests experimentally. It was shown that different mechanical behaviors could be obtained for different implicit function parameters. In this research, to assess the mechanical behavior of printed scaffolds in terms of the strain-stress curves on, two approaches were presented: equivalent volume and finite element-based volume. Results of strain-stress curves showed that the finite-element based approach predicts a higher level of stress. Moreover, the biological response of composite scaffolds in terms of cell viability, cell proliferation, and cell attachment was investigated. In this vein, a dynamic cell culture system was designed and fabricated, which improves mass transport through the composite scaffolds and applies mechanical loading to the cells, which helps cell proliferation. Moreover, the results of the novel composite scaffolds were compared to those without alginate, and it was shown that the composite scaffold could create more viability and cell proliferation in both dynamic and static cultures. Also, it was shown that scaffolds in dynamic cell culture have a better biological response than in static culture. In addition, scanning electron microscopy was employed to study the cell adhesion on the composite scaffolds, which showed excellent attachment between the scaffolds and cells.