The effects of external electric fields (EFs) on the magnetic state and substrate-mediated magnetic coupling between Mn dimers on Cu(1 1 1) have been studied using a first-principles theoretical method. The calculations show that a change in the ground-state magnetic order, from antiferromagnetic (AF) to ferromagnetic (FM), can be induced within an isolated Mn2 on Cu(1 1 1) by applying a moderately strong EF of about 1 V Å⁻¹. The magnetic exchange coupling between pairs of dimers displays Ruderman-Kittel-Kasuya-Yosida-like oscillations as a function of the interdimer distance, which depend significantly on the magnetic order within the dimers (FM or AF) and on their relative orientation on the surface. Moreover, it is observed that applying EFs allows modulation of the exchange coupling within and between the clusters as a function of the intercluster distance. At short distances, AF order within the dimers is favoured even in the presence of EFs, while for large distances the EF can induce a FM order. EFs pointing outwards and inwards with respect to the surface favour parallel and antiparallel magnetic alignment between the dimers, resspectively. The dependence of the substrate-mediated interaction on the magnetic state of Mn2 is qualitatively interpreted in terms of the differences in the scattering of spin-polarized surface electrons.