Carbon dioxide (CO2) conversion to value-added chemicals is an attractive solution to reduce globally accelerating CO2 emissions. Among the non-precious and abundant metals tested so far, copper (Cu) is one of the best electrocatalysts to convert CO2 into more than thirty different hydrocarbons and alcohols. However, the selectivity for desired products is often too low. We present a computational investigation of the effects of nanostructuring, doping, and support on the activity and selectivity of Cu-Sn catalysts. Density functional theory calculations were conducted to explore the possibility of using small Cu-Sn clusters, Cu4-nSnn (n = 0-4), isolated or supported on graphene and γ-Al2O3, to activate CO2 and convert it to carbon monoxide (CO) and formic acid (HCOOH). First, a detailed analysis of the structure, stability, and electronic properties of Cu4-nSnn clusters and their ability to absorb and activate CO2 was considered. Then, the kinetics of the gas phase CO2 direct dissociation on Cu4-nSnn to generate CO was determined. Finally, the mechanism of electrocatalytic CO2 reduction to CO and HCOOH on Cu4-nSnn, Cu4-nSnn/graphene and Cu4-nSnn/γ-Al2O3 was computed. The selectivity towards the competitive electrochemical hydrogen evolution reaction on these catalysts was also considered. The Cu2Sn2 cluster suppresses the hydrogen evolution reaction and is highly selective towards CO, if unsupported, or HCOOH if supported on graphene. This study demonstrates that the Cu2Sn2 cluster is a potential candidate for the electrocatalytic conversion of the CO2 molecule. Moreover, it identifies insightful structure-property relationships in Cu-based nanocatalysts, highlighting the influence of composition and catalyst support on CO2 activation.