The Ar+-irradiated molybdenum-disulfide (MoS2) surface is studied by means of Raman spectroscopy and first-principles calculation. This experimental study reveals that Ar+ irradiation gives rise to satellite peaks at the lower-frequency side of the Raman-active E-2g(1) and A(1g) modes of MoS2 and a new peak at approximately 450 cm(-1). We calculate the phonon modes and Raman spectra of defective MoS2 systems from first principles, and show that Mo and S vacancies give rise to such satellite peaks. These satellite peaks are a modulation of the E-2g(1) and A(1g) modes, described in terms of localization and scattering of vibration modes. The new peak at 450 cm(-1), however, is a unique signature of the S vacancy. At low irradiation doses, the S vacancy is the dominant defect, whereas for large irradiation doses, the satellite peaks overshadow the MoS2 peaks, which we show to be typical for the Mo vacancy and MoS6 vacancy cluster. We thus show that Raman spectroscopy can be used not only to observe defects in two-dimensional materials, but also to identify the type of the defects.