This paper investigates numerically the effect of damage evolution on adiabatic shear banding (ASB) formation and its transition to fracture during high-speed blanking of 304 stainless steel sheets. A structural-thermal-damage-coupled finite element (FE) analysis is developed in LS-DYNA considering the modified Johnson–Cook thermo-viscoplastic model for both plasticity flow rule and damage law, while further, a temperature-dependent fracture criterion is implemented by introducing a critical temperature. The modeling approach is initially validated against experimental data regarding the fracture profile and ASB width. Next, FE simulations are conducted to examine the effect of strain rate and temperature dependence on damage law, while the effect of damage coupling is also evaluated, aiming to highlight the connection between thermal and damage softening and attribute them a specific role regarding ASB formation and transition to fracture. Also, the influence of dynamic recrystallization (DRX) softening is studied macroscopically, while further, a parametric analysis of the Taylor–Quinney coefficient is conducted to highlight the effect of plastic work-to-internal heat conversion efficiency on ASB formation. The results revealed that the implementation of damage coupling reacts to reduced ASB width and provides an S-shaped fracture profile, while it also decreases the peak force and results in an earlier fracture. Both findings are enhanced when accounting further for DRX softening and a higher value of the Taylor–Quinney coefficient. Finally, the simulations indicated that thermal softening precedes damage softening, showing that the temperature rise is responsible for ASB initiation, while instead, damage evolution drives ASB propagation and fracture.