The pronounced effects of the composition of four-atom monometallic Cu and Pd and bimetallic CuPd clusters and the support on the catalytic activity and selectivity in the oxidative dehydrogenation of cyclohexene are reported. The ultra-nanocrystalline diamond supported clusters are highly active and dominantly produce benzene; some of the mixed clusters also produce cyclohexadiene, which are all clusters with a much suppressed combustion channel. The also highly active TiO2-supported tetramers solely produce benzene, without any combustion to CO2. The selectivity of the zirconia-supported mixed CuPd clusters and the monometallic Cu cluster is entirely different; though they are less active in comparison to clusters with other supports, these clusters produce significant fractions of cyclohexadiene, with their selectivity towards cyclohexadiene gradually increasing with the increasing number of copper atoms in the cluster, reaching about 50% for Cu3Pd1. The zirconia-supported copper tetramer stands out from among all the other tetramers in this reaction, with a selectivity towards cyclohexadiene of 70%, which far exceeds those of all the other cluster-support combinations. The findings from this study indicate a positive effect of copper on the stability of the mixed tetramers and potential new ways of fine-tuning catalyst performance by controlling the composition of the active site and via cluster-support interactions in complex oxidative reactions under the suppression of the undesired combustion of the feed.