Asphalt mixture stands as one of the extensively utilized materials within the realm of road engineering. Fibers have the remarkable ability to substantially enhance the road performance of asphalt mixtures. The influence of fibers on the physical and mechanical properties of asphalt mixtures, along with the microscopic strengthening mechanism, has drawn the attention of numerous scholars. In this research, the basalt fiber reinforced asphalt mixture (BFRAM) was selected as the subject of study. A series of material tests on the BFRAM were conducted to investigate the impact of basalt fibers on the physical and mechanical properties of the asphalt mixture, including bulk density, stability, flow value, and compressive strength. Based on the discrete element method, the entire process of crack formation, development, and failure of the asphalt mixture under uniaxial compression was simulated. This simulation served to uncover the microscopic strengthening mechanism of the BFRAM. The results indicated that as the fiber content increased, the bulk density and voids filled with asphalt with 6 mm and 9 mm fiber content first decreased, then increased, and finally decreased again. For 12 mm fiber content, the bulk density and voids filled with asphalt first increased and then decreased. Conversely, the void content of asphalt mixture and the asphalt-aggregate ratio showed an opposite trend, while Marshall stability consistently increased. The compressive strength of the asphalt mixture initially rises and then falls. When the fiber content reached 0.3%, the stability and compressive strength of the asphalt mixture increased by 23.6% and 43.3% respectively, in comparison to the asphalt mixture without fiber. From the perspective of microscopic mechanism analysis, the adhesion between asphalt aggregates was significantly strengthened after the addition of fibers. When the fiber content was less than 0.3%, the number of cracks, crack width, and damage degree of the asphalt mixture were notably improved. However, when the fiber content exceeded 0.3%, fiber agglomeration occurred. This phenomenon reduced the number of contacts within the mixtures, leading to a decrease in the compressive strength of the BFRAM.