Here, we theoretically screened and explored the catalytic mechanism of electrocatalytic CO2 reduction reaction (eCO2RR) on Ti@Cu single atom alloy (SAA) and its oxidized variants (O-Ti@Cu and OH-Ti@Cu), focuseing on the effect of surface oxygen species on catalytical activity and selectivity under varying acidity and applied potential. Thermodynamically, Ti@Cu can be easily synthesized and oxidized in an aqueous solvent, as indicated by its low formation energy (-1.60 eV) and free energy (-0.92 eV) for oxidation. Catalytically, the introduction of bystander oxygen species facilitates the hydrogenation of residual *O after the generation of C2 products in eCO2RR on the Ti@Cu surface. This results in an inclination for eCO2RR on Ti@Cu to predominantly produce C1 product CH4 (ΔGRDS = 0.51 eV), while on the O-Ti@Cu and OH-Ti@Cu surfaces, there is a respective tendency towards the production of C2 products CH2CH2 (ΔGRDS = 0.51 eV) and CH3COOH (ΔGRDS=0.45 eV). Importantly, the potential required for eCO2RR on pure Ti@Cu is 0.70 V, notably lower than the 0.86 V needed for the *O hydrogenation. This confirms the stability of oxygen species (*O and *OH) on Ti@Cu under electrochemical conditions. Furthermore, the catalytic mechanism under varying electrochemical conditions (different potential and acidity) revealed that Ti@Cu favored CH4 production at pH = 1, 7, and 13, whereas both O-Ti@Cu and OH-Ti@Cu surfaces tended to produce CH2CH2 and CH3COOH at pH 1 and CH4 at pH = 7 and 13. This study contributes to our understanding of the catalytic mechanism of eCO2RR under realistic electrochemical conditions.