The uniaxial compression experiment of red sandstone is observed simultaneously by using acoustic emission and digital speckle correlation methods. The deformation evolution of red sandstone is divided into microfracture random expansion stage, deformation localization stage, subinstability stage, and instability failure stage. Green’s function and dispersion curve of each stage are obtained from the noise data picked up by acoustic emission equipment, and the dispersion characteristics of each evolution stage are analyzed. The results show the following: (1) In the stage of random propagation of microcracks, the noise in the low frequency range passes through at a higher phase velocity, the phase velocity changes periodically, the correlation coefficient is high at the initial time, and the variation trend of frequency dispersion curve is relatively consistent. (2) In the deformation localization stage, the frequency range without zero phase velocity moves to the high frequency range, and the phase velocity changes periodically. (3) In the subinstability stage, dense phase velocity zeros appear on the dispersion curve image, the dispersion curve tends to be disordered, various indicators change obviously, and the correlation coefficient decreases rapidly. (4) In the unstable failure stage, the fracture evolution is completed, and the variation trend of each index of the frequency dispersion curve is consistent. (5) The size and difference of the sensitive kernel function of the two layers are related to the evolution region of the fracture. The sensitivity kernel value of the medium layer where the fracture evolves is high, and the longer the evolution time, the greater the difference.