A library of structurally related coumarins was generated through synthesis reactions and chemical modification reactions to obtain derivatives with antiproliferative activity both in vivo and in vitro. Out of a total of 35 structurally related coumarin derivatives, seven of them showed inhibitory activity in in vitro tests against Taq DNA polymerase with IC50 values lower than 250 μM. The derivatives 4-(chloromethyl)-5,7-dihydroxy-2H-chromen-2-one (2d) and 4-((acetylthio)methyl)-2-oxo-2H-chromen-7-yl acetate (3c) showed the most promising anti-polymerase activity with IC50 values of 20.7 ± 2.10 and 48.25 ± 1.20 μM, respectively. Assays with tumor cell lines (HEK 293 and HCT-116) were carried out, and the derivative 4-(chloromethyl)-7,8-dihydroxy-2H-chromen-2-one (2c) was the most promising, with an IC50 value of 8.47 μM and a selectivity index of 1.87. In addition, the derivatives were evaluated against Saccharomyces cerevisiae strains that report about common modes of actions, including DNA damage, that are expected for agents that cause replicative stress. The coumarin derivatives 7-(2-(oxiran-2-yl)ethoxy)-2H-chromen-2-one (5b) and 7-(3-(oxiran-2-yl)propoxy)-2H-chromen-2-one (5c) caused DNA damage in S. cerevisiae. The O-alkenylepoxy group stands out as that with the most important functionality within this family of 35 derivatives, presenting a very good profile as an antiproliferative scaffold. Finally, the in vitro antiretroviral capacity was tested through RT-PCR assays. Derivative 5c showed inhibitory activity below 150 μM with an IC50 value of 134.22 ± 2.37 μM, highlighting the O-butylepoxy group as the functionalization responsible for the activity.