Nuclear power is a high-quality clean energy source, but nuclear waste is generated during operation. The waste continuously releases heat during disposal, increasing the adjoining rock temperature and affecting the safety of the disposal site. Basalt is widely considered a commonly used rock type in the repository. This study of basalt’s mechanical characteristics and damage evolution after thermal damage, with its far-reaching engineering value, was conducted by combining experimental work and theory. Uniaxial compression tests were conducted on basalt exposed to 25 °C, 500 °C, 700 °C, 900 °C, and 1100 °C conditions, and acoustic emission (AE) equipment was utilized to observe the acoustic emission phenomenon during deformation. This study was carried out to examine the mechanical characteristics, the sound emission features, the progression of damage laws, and the stress–strain framework of basalt after exposure to different types of thermal harm. As the temperature rises, the rock’s maximum strength declines steadily, the peak strain rises in tandem, the rock sample’s ductility is augmented, the failure mode changes from shear to tensile failure, and cracks in the failure area are observed. At room temperature, the acoustic emission signal is more vigorous than in the initial stage of rock sample loading due to thermal damage; however, after the linear elastic stage is entered, its activity is lessened. In cases where the rock approaches collapse, there is a significant surge in acoustic emission activity, leading to the peak frequency of acoustic emission ringing. The cumulative ring count of acoustic emission serves as the basis for the definition of the damage variable. At room temperature, the damage evolution of rock samples can be broken down into four distinct stages. This defined damage variable is more reflective of the entire failure process. After exposure to high temperatures, the initial damage of the rock sample becomes more extensive, and the damage variable tends to be stable with strain evolution. The stress–strain constitutive model of basalt deformation is derived based on the crack axial strain law and acoustic emission parameters. A powerful relationship between theoretical and experimental curves is evident.