Based on a CeO2–Al2O3 support (CA-T) prepared by two-step incipient wetness impregnation (T-IWI) method, an efficient CuO catalyst supported on CA-T (Cu/CA-T) was successfully developed, which showed better catalytic performance in CO oxidation and NO reduction by CO (NO + CO reaction) together with higher thermal stability than the CuO catalyst loaded on conventional CeO2–Al2O3 support (Cu/CA). Based on the results of HAADF-STEM, Raman spectra, electron paramagnetic resonance, X-ray absorption spectroscopy, ex situ and quasi in situ X-ray photoelectron spectroscopy, in situ diffuse reflectance infrared Fourier transform spectroscopy, and dynamic oxygen storage capacity (OSC) testing, etc., the microstructure of CuO–CeO2–Al2O3 catalysts, especially the state of Cu species, was systemically investigated. The mechanisms of CO oxidation and NO + CO reactions on Cu/CA and Cu/CA-T catalysts were collaboratively revealed. It was found that the CA-T support with smaller CeO2 particles could facilitate the formation of more highly dispersed CuOx clusters with better redox property. In CO oxidation, more active Cu+ species could be formed on Cu/CA-T under reaction conditions due to the higher reducibility of CuOx clusters on CeO2, which contributed to its superior CO removal efficiency. After aging, a significant decrease in CO oxidation activity was observed on Cu/CA catalyst, which was mainly resulted from the disappearance of highly dispersed CuOx clusters. In clear contrast, for aged Cu/CA-T catalyst, the highly dispersed CuOx clusters could be well preserved, well explaining its much higher catalytic activity and thermal stability than the aged Cu/CA counterpart as probed by the CO oxidation reaction. In NO + CO reaction, besides the formation of more Cu+ sites for CO adsorption and activation, much higher OSC function was also achieved on the Cu/CA-T catalyst. This was due to the higher concentration of surface oxygen vacancies and moderate strength of CuOx–CeO2 interaction on Cu/CA-T, which could effectively promote the NO dissociation into [N] for N2 formation and the transfer of dissociated [O] to CO@Cu+ sites to complete the CO depletion.