Asphalt binder is a complex mixture of dark brown polymers composed of hydrocarbons with generally poor fire resistance. To improve its flame retardancy when used in tunnel asphalt pavements, a new inorganic flame-retardant filler (FR) containing magnesium hydroxide, aluminum hydroxide, inorganic phosphate, and melamine salt was explored. Thereafter, limiting oxygen index (LOI) and smoke suppression tests for the flame-retarded asphalt binder (FRA) mastics mixed with FR and styrene-butadiene-styrene (SBS) copolymer asphalt binder were conducted. Thermogravimetric (TG) and differential scanning calorimetry (DSC) curves for the FRA were correspondingly generated. Based on the TG data, the reaction function g(α), apparent activation energy Ea, and pre-exponential factor A were quantitatively evaluated using kinetic analysis. In addition, a Fourier transform infrared spectrometry (FTIR) test was utilized to assess the effects of the presence of FR on the chemical composition of the asphalt binder. Dynamic shear rheometer (DSR) tests were also performed to evaluate the rheological behavior of FRA. Results show that the presence of the FR significantly reduced the LOI and improved the smoke suppression during combustion of the asphalt binder mastics. The presence of FR was found to increase the Ea and the complexity of the combustion reaction, thereby improving the flame retardancy of the asphalt binder. FTIR analysis indicated that the presence of FR did not induce any strong chemical reactions to significantly impact or alter the functional groups of the asphalt binder. Furthermore, it was also observed that the rutting parameter and critical failure temperature of FRA increased with the addition of FR due to the stiffening effect of the solid FR particles.