The process of foaming poly(caprolactone)-based composite materials using supercritical carbon dioxide was analyzed, especially in terms of the biocompatibility of the resultant materials. The influence of foaming process conditions and composite material properties on the functional properties of polymer solid foams, intended for artificial scaffolds for bone cell culture, was investigated. The relationship between wettability (contact angle) and water absorption rate as a result of the application of variable conditions for the production of porous structures was presented. For the evaluation of potential cytotoxicity, the MTT and PrestoBlue tests were carried out, and animal cells (mouse fibroblasts) were cultured on the materials for nine days. There was no toxic effect of composite materials made of poly(caprolactone) containing porogen particles: hydroxyapatite, crystalline nanocellulose, and graphene oxide on cells. The desired effect of the porogens used in the foaming process on the affinity of cells to the resultant material was demonstrated. The tested materials have been shown to be biocompatible and suitable for applications in biomedical engineering.