To investigate the crack resistance of typical asphalt mixtures under salt erosion and dynamic water conditions, direct tensile tests combined with the digital image correlation (DIC) method were conducted to examine the tensile strength evolution and principal strain field development of AH-70, SBS-modified, and rubber-modified asphalt mixtures. The results show that all the mixtures exhibited ductile failure characteristics, with cracks mostly initiating at the binder-aggregate interface and propagating along the strain concentration zones. Dynamic water cycling markedly induced interfacial stripping and moisture damage in the AH-70 asphalt mixture, whereas static saline dry-wet cycling further exacerbated pore expansion. After 20 d of dry-wet cycling in a 20% salt solution, the tensile strength and strain energy density of the AH-70 asphalt mixture decreased by 41.6% and 57.8%, respectively, and these values decreased by 56.1% and 69.4% after dynamic water cycling. In contrast, the SBS- and rubber-modified asphalt mixtures showed superior structural stability and durability. High salinity and dry-wet cycling jointly weakened the toughness of the asphalt mixtures. However, owing to its excellent viscoelasticity, rubber-modified asphalt retained a higher residual strength and energy absorption capacity, exhibiting notable advantages in crack and stripping resistance.