In our newly developed gas-hydrate cluster ion source, a vapor of water bubbling with carbon dioxide (CO2) gas was ejected through a nozzle into a vacuum region, and mixed beams of water clusters and carbon dioxide-hydrate clusters were produced by adiabatic expansion. According to time-of-flight measurements, the largest water clusters consisted of approximately 2800 molecules at a vapor pressure of 0.3 MPa. Also, the largest mixed clusters contained approximately 2000 molecules. Copper and silicon substrates were irradiated by the water cluster ions as well as carbon dioxide-hydrate cluster ions. X-ray photoelectron spectroscopy measurements showed that carbon was included in the Cu and Si substrates irradiated by the carbon dioxide-hydrate cluster ions, and a chemical shift owing to the formation of carboxyl radicals occurred on the Cu surface. Furthermore, the Cu surface was sputtered, and the sputtering depth was larger than the distance penetrated by the water cluster ion irradiation. Therefore, the formation of carboxyl radicals played an important role in the sputtering of the Cu surface, which occurred effectively in carbon dioxide-hydrate cluster ion irradiation.