Selective hydrogenation of carbon dioxide (CO 2 ) into value-added chemicals via highly efficient catalysts is of great significance in CO 2 conversion and utilization. Here, taking Cu N /MoS 2 /Ag(111) heterostructures (N = 1−8) as prototypical examples, we theoretically establish a concept of a dynamically magic single-cluster catalyst (DMSCC) for high-efficient selective hydrogenation of CO 2 to CH 3 OH. It is found that, though Cu 2 and Cu 8 in the gas phase are well recognized as magic clusters due to closed-shell electronic structures, Cu 3 and Cu 7 become new magic clusters when deposited on MoS 2 /Ag(111) due to their high-symmetric structures and strong Cu−S ionic bonding. Moreover, the dynamic evolution of the geometric structure of the Cu 3 species with an alkali-metal-like electronic feature and the d z 2 frontier orbital accounts for its highly selective catalytic activity for CO 2 reduction to CH 3 OH rather than HCOO with a low rate-limiting reaction barrier of ∼1.10 eV. However, the deposited Cu 7 is relatively highly inert toward CO 2 activation because of its halogen-element-like electronic characteristics. The present findings on DMSCC are expected to be constructive in design and fabrication of highly efficient single-atomic-scale catalysts for CO 2 activation and conversion.