Optimising the supported modes of atom or ion dispersal onto substrates, to synchronously integrate high reactivity and robust stability in catalytic conversion, is an important yet challenging area of research. Here, theoretical calculations first show that three-coordinated copper (Cu) sites have higher activity than four-, two- and one-coordinated sites. A site-selective etching method is then introduced to prepare a stacked-nanosheet metal-organic framework (MOF, CASFZU-1)-based catalyst with precisely controlled coordination number sites on its surface. The turnover frequency value of CASFZU-1 with three-coordinated Cu sites, for cycloaddition reaction of CO2 with epoxides, greatly exceed those of other catalysts reported to date. Five successive catalytic cycles reveal the superior stability of CASFZU-1 in the stacked-nanosheet structure. This study could form a basis for the rational design and construction of highly efficient and robust catalysts in the field of single-atom or ion catalysis.