In order to study the creep behavior of deep soft rock, gritstone was chosen as the research subject, and a rock triaxial rheometer (Rock 600-50) and acoustic emission (AE) system (SH-II) were used to carry out the grade unloading confining pressure creep test under a high-stress level. The test results showed that the lateral creep behavior of the gritstone was more prominent than the axial creep under the initial high confining pressure. Under the same confining pressure, the creep strain rate (the direction the same as strain) of the gritstone decreases with the increase in axial pressure. As shown by the AE count, AE signals were generated throughout the entire test process, indicating that the creep was a “microdynamic” process. The creep behavior was characterized by a significant confining pressure effect. As the confining pressure was decreased, the degree of creep increases significantly. During the test, the AE energy increased on the whole but decreases during the creep phase. During the entire test process, the overall energy in the constant deviatoric stress grade unloading of the confining pressure was 45% higher than that in the constant axial pressure grade unloading. The degree of failure of the rock was different in these two unloading creep tests, and the constant axial pressure grade unloading of the confining pressure entails greater damage than the constant deviatoric stress grade unloading of the confining pressure. The main reason was that the former had a lower confining pressure level and longer creep process than the latter, and the sample was mainly characterized by creep damage and large cumulative damage, while the latter features mainly unloading damage. Through the inversion of the Burgers constitutive model and nonlinear damage constitutive model for the creep test curve, the nonlinear constitutive equation can better fit the accelerated creep stage, which suggested that this model can describe the accelerated creep characteristics of the high-stress soft rock.