The critical point of rock mass transition from stable to unstable states is significant for the prevention and control of rock engineering hazards. This study explored the precursor characteristics of instability in sandstone containing prefabricated fractures and intact sandstone based on the critical slowing down (CSD) theory. The results demonstrated that as the input energy drove the dissipation energy dynamic system toward the critical point of two states, the CSD phenomenon appeared, which was manifested by the sudden increase in CSD time series metrics (skewness, kurtosis, and coefficient of variation) and autoregressive model metrics (variance and autocorrelation coefficient). The CSD characteristics of different dissipation energy dynamical systems were different, resulting in different times of CSD phenomena for distinct systems. In addition, the angle of the sandstone fracture affected the characteristics of the dissipation energy dynamical system and hence the appearance time of the precursor information. The precursor time of the sandstone containing 45° parallel fractures appeared earliest among all rock samples, and the ratio of the appearance time of the precursor point to the failure time of all rock samples reached more than 80%, which had good timeliness. The stress at the precursor point reached more than 80% of the peak stress, which corresponded to the plastic stage in the loading process, indicating that the CSD indicators constitute an effective monitoring index, which can provide an important reference for the stability monitoring and early warning of the field rock project.