This study is to reveal internal relationships between cumulative damage effects of rock blasting and acoustic variation characters of rock mass. In this study, a small dose of blasting was conducted for ten times on the surrounding rock in underground engineering. Then in-situ acoustic measurement was carried out to analyze the corresponding damage of rock mass. Based on the fast Fourier transform (FFT), attenuation characteristics of the acoustic wave were discussed when propagating in rock mass with blasted damage. Meanwhile, this study also investigated the effect of blasting times on variation laws of acoustic parameters of rock mass, such as the dominant frequency and maximum amplitude in the frequency domain. In addition, the influence factors, for example, the thickness of the broken zone, the distance between transducers, the distance from the explosive source, were all analyzed as well. Research results show that high-frequency components of acoustic signals were absorbed gradually with increasing and extending blasting rock cracks, while the proportion of low-frequency components grew up constantly with the addition of blasting times. At the same time, the dominant frequency was shifted in the low-frequency direction. Furthermore, the distortion degree of frequency spectrum curves increased. It is found that both the dominant frequency ratio and the maximum amplitude ratio in the frequency domain declined nonlinearly. Moreover, the latter was more sensitive to blasting damage than the former. The variability of rock mass frequency spectrum became weakening with increasing the distance from the explosive source. The increase of the dominant frequency and the attenuation of the maximum amplitude in the frequency domain were substantially significant with the increase of the distance between transducers. Therefore, this study provides a valuable reference to enrich and improve the acoustic method for cumulative damage effects of rock mass blasting.