We study the light scattered from randomly rough, one-dimensional, self-affine fractal silver surfaces with nanoscale lower cutoff illuminated by s- or p-polarized Gaussian beams a few micrometers wide. By means of rigorous numerical calculations based on the Green's theorem integral equation formulation (GTIEF), we obtain both the far- and near-field scattered intensities. The influence of diminishing the size of the fractal lower-scale irregularities (from approximately 50 nm to a few nanometers) is analyzed in the case of both single realization and ensemble-average magnitudes. For s polarization, variations are small in the far field, being significant only in the higher-spatial-frequency components of evanescent character in the near field. In the case of p polarization, however, the nanoscale cutoff has remarkable effects stemming from the roughness-induced excitation of surface-plasmon polaritons. In the far field, the effect is noticed both in the speckle pattern variation and in the decrease of the total reflected energy upon ensemble averaging, as a result of increased absorption. In the near field, more efficient excitation of localized optical modes is achieved with smaller cutoff, which in turn leads to huge surface electric field enhancements.