The angle-resolved energy spectra of the electrons emitted from a metal surface during specular reflection of heavy ions have been studied by means of the first-order, time-dependent perturbation theory, with the electron states obtained from a finite step-barrier potential model. The surface response has been described by the dielectric formalism within the specular reflection model, where the local-field correction and the plasmon-pole approximation have been used for the dielectric function in the cases of low and high ion velocities, respectively. The ion trajectory has been evaluated based on the surface continuum potential and the ion image potential, whereas the screening of the ion by the bound electrons has been taken into account by means of the Brandt-Kitagawa model. It has been found that the electron spectra are dominated by the decay of surface plasmons for fast incident ions, whereas the electron emission is dominated by the single-electron excitation mechanism for slow incident ions.