To explore the development mechanism of cracks in the process of rock failure, triaxial compression tests with simultaneous acoustic emission monitoring were performed on granite specimens using the MTS rock mechanics test system. The frequency-domain information of the acoustic emission signal was obtained by the fast Fourier transform. The Gutenberg–Richter law was used to calculate the acoustic emission signals and obtain the b-value dynamic curve in the loading process. Combined with the stiffness curve of granite specimens and acoustic emission signal in the time domain and frequency domain, the crack development characteristics in different stages were analyzed. The results showed that the acoustic emission signals of granite samples under triaxial compression can be divided into four stages: quiet period 1, active stage 1, quiet period 2, and active stage 2. b-value attained its maximum value in the active phase 2 when it is close to the sample loss, and then drops rapidly, which means the propagation of cracks and the formation of large cracks. The acoustic emission signal’s dominant frequency was not more than 500 kHz, mostly concentrated in the medium-frequency band (100–200 kHz), which accounted for more than 80%. The proportion of signals in each frequency band can reflect the distribution of the three kinds of cracks, while the change in low-frequency signals can reflect the breakthrough of microcracks and the formation time of macrocracks in granite samples. By fully analyzing the characteristics of acoustic emission signals in the time domain and frequency domain, the time and conditions of producing large cracks can be determined accurately and efficiently.