The surface properties of fibers significantly influence fiber-reinforced asphalt mastic (FRAM) performance. However, the impact of composite-modified basalt fiber (BF) on basalt fiber-reinforced asphalt mastic (BFRAM) remains unclear. This study examines the effects of acid-base/KH550 modified BFs on BFRAM performance, providing an experimental basis for further optimization. Tests included SEM and fiber leakage for BFs and separation, physical properties, DSR, and DMA for BFRAMs. The research indicates that (1) Composite modification enhances the fiber’s surface roughness, activity, oil-holding properties, and compatibility with SBS-modified asphalt. (2) Due to differences in acid-base etching, acid etching combined with KH550 promotes a more uniform and extensive coupling reaction with the BFs. In contrast, alkali etching with KH550 facilitates a deeper, localized reaction. (3) Composite modification of the BFs significantly improves the high-temperature rheological properties of the BFRAMs, with acid-base etching making the grafting reaction between the fiber and coupling agent more pronounced. At a test temperature of 82°C, the rutting factor of BFRAMs containing composite-modified (acid-etched + KH550) BFs is 2.7 times that of asphalt mastic without BFs. (4) The glass transition temperature of BFRAMs modified by acid etching and KH550 is 4.9°C lower than that of the original asphalt mastic, proving that composite-modified BFs enhance the low-temperature elastic deformation capacity of the BFRAMs.