In recent years, the linear amplitude sweep test (LAS) and the time sweep (TS) test under dynamic shear are widely used to evaluate the damage resistance of paving asphalt. This paper attempts to demonstrate the possibility of using the LAS test as the accelerated fatigue protocol for damage resistance estimation of asphalt from perspectives of crack initiation and propagation. Both the finite element (FE) simulation and experimental work based on fracture mechanics are conducted for this purpose, followed by the verification on the traditional TS fatigue test. The FE model of the cylindrical asphalt sample is created by means of the FRANC2d/L software to identify the cracking mode under the crack propagation phase. The LAS test results show that the damage evolution behavior follows the two-phase crack growth (TPCG) model and the crack propagation is governed by mode-I cracking, which is consistent to the FE-based numerical simulation. The TS test results show that the TPCG model in the LAS protocol can be utilized to reasonably distinguish the crack initiation and propagation resistance of different asphalts. The polymer modification on asphalt can significantly improve its fatigue damage resistance.