The purpose of this study was to analyze in vitro the biological effects on human dental pulp stem cells triggered in response to substances leached or dissolved from two experimental cements for dental pulp capping. The experimental materials, based on extracts from Copaifera reticulata Ducke (COP), were compared to calcium hydroxide [Ca(OH)2] and mineral trioxide aggregate (MTA), materials commonly used for direct dental pulp capping in restorative dentistry. For this, human dental pulp stem cells were exposed to COP associated or not with Ca(OH)2 or MTA. Cell cytocompatibility, migration, and differentiation (mineralized nodule formation (Alizarin red assay) and gene expression (RT-qPCR) of OCN, DSPP, and HSP-27 (genes regulated in biomineralization events)) were evaluated. The results showed that the association of COP reduced the cytotoxicity of Ca(OH)2. Upregulations of the OCN, DSPP, and HSP-27 genes were observed in response to the association of COP to MTA, and the DSPP and HSP-27 genes were upregulated in the Ca(OH)2 + COP group. In up to 24 h, cell migration was significantly enhanced in the MTA + COP and Ca(OH)2 + COP groups. In conclusion, the combination of COP with the currently used materials for dental pulp capping [Ca(OH)2 and MTA] improved the cell activities related to pulp repair (i.e., cytocompatibility, differentiation, mineralization, and migration) including a protective effect against the cytotoxicity of Ca(OH)2.