The mechanism of the copper(I)-catalyzed cyclopropanation reaction for methyl diazoacetate with both (Z)- and (E)-but-2-ene stereoisomers has been studied using the 6-311++G(d,p) basis set by means of M06-2X and O3LYP functionals. According to both methods, the rate-limiting step is the formation of a copper-carbene intermediate, formed by association between methyl diazoacetate and bis(acetonitrile)-copper(I) ion with the concomitant extrusion of dinitrogen. Cis/trans diastereoselectivity for the cyclopropanation reaction of a 1,2-disubstituted alkene ((Z)-but-2-ene) has been theoretically studied for the first time through the proper location of transition states on the potential-energy surface with the O3LYP method, since no transition structures could be found with the M06-2X functional due to the extreme flatness of the potential-energy surface. The calculated stereoselectivities involving two acetonitrile ligands or one dichloromethane molecule show qualitative agreement with experimental data. This study allows attributing the origin of the selectivity to steric interactions between the ligands of the catalyst system and the olefin substituents. The comparison between the corresponding activation barriers for the direct insertion step shows a higher reactivity for the Z stereoisomer of but-2-ene, consistently with the larger reactant destabilization through steric interactions.