The x-ray irradiation effect on the resistivity and dielectric constant of the dimer-Mott insulator κ-(BEDT-TTF)2-Cu2(CN)3 has been investigated. The x-ray irradiation, producing defects and random potentials mainly in anion molecular layers, reduces the resistivity. We observed two anomalous peaks in the temperature dependence of the dielectric constant with an increasing irradiation time. One of the peaks, which is originally observable showing a Curie-Weiss behavior with a strong frequency dependence, shifts to lower temperatures and decreases in intensity. We found an additional peak that emerges after irradiation of ≈250 h and becomes dominant with irradiation. The qualitative differences in the change in the anomalies suggest that the additional anomaly is directly due to the anion defects and that the change in the original anomaly is due to the segmentation of local polar regions and the decrease in the size of domains. These results are explained by the charge degrees of freedom in the BEDT-TTF dimer.