Self-extinction of a species due to evolution is the consequence of the event whenever a mutant prey closer to extinction boundary are at advantage with respect to the resident. In response to the threat of predation, the foraging effort of prey can be considered as an evolving trait. The effects of harvesting in the long-term evolutionary scenario was not investigated theoretically in any of the previous models studied before. Hence we incorporate constant-effort prey and predator harvesting in the model. We also considered individual logistic growth of predator. Our model exhibits i) Evolutionary suicide via a saddle-node bifurcation where, evolution of foraging of prey results in lower forager mutant invasion consequently resulting extinction of prey and ii) Evolutionary reversal via a subcritical Hopf bifurcation where the opposite values of selection gradient at the two alternative demographic attractors causes the cyclic evolution of prey. These contrasting evolutionary scenario is observed due to variation in the choices of harvesting parameters keeping the other parameters fixed which makes the model a study of interest.