High-surface-quality amorphous carbon (a-C) optical coatings with a thickness of 45 nm, deposited by magnetron sputtering on a silicon substrate, were irradiated by the focused beam of capillary-discharge Ne-like Ar XUV laser (CDL = capillary-discharge laser; XUV = extreme ultraviolet, i.e., wavelengths below 100 nm). The laser wavelength and pulse duration were 46.9 nm and 1.7 ns, respectively. The laser beam was focused onto the sample surface by a spherical Sc/Si multilayer mirror with a total reflectivity of about 30%. The laser pulse energy was varied from 0.4 µJ to 40 µJ on the sample surface. The irradiation was carried out at five fluence levels between 0.1 J/cm 2 and 10 J/cm 2 , accumulating five different series of shots, i.e., 1, 5, 10, 20 and 40. The damage to the a-C thin layer was investigated by atomic force microscopy (AFM) and Nomarski differential interference contrast (DIC) optical microscopy. The dependence of the single-shot-damaged area on pulse energy makes it possible to determine a beam spot diameter in the focus. Its value was found to be equal to (23.3±3.0) µm using AFM data, assuming the beam to have a Gaussian profile. Such a plot can also be used for a determination of single-shot damage threshold in a-C. A single-shot threshold value of 1.1 J/cm 2 was found. Investigating the consequences of the multiple-shot exposure, it has been found that an accumulation of 10, 20 and 40 shots at a fluence of 0.5 J/cm 2 , i.e., below the single-shot damage threshold, causes irreversible changes of thin a-C layers which can be registered by both the AFM and the DIC microscopy. In the center of the damaged area, AFM shows a-C removal to a maximum depth of 0.3, 1.2 and 1.5 nm for 10-, 20-and 40-shot exposure, respectively. A Raman micro-probe does not indicate any change in the structure of the remaining a-C material. The erosive behavior reported here contrasts with the material expansion observed earlier [L. Juha et al., Proc. SPIE 5917, 91 (2005)] on an a-C sample irradiated by a large number of femtosecond pulses of XUV high-order harmonics (HHs).