(1) Background: Together with treatment protocols, viscoelastic tests are widely used for patient care. Measuring at broader ranges of deformation than currently done will add information on a clot’s mechanical phenotype because fibrin networks follow different stretching regimes, and blood flow compels clots into a dynamic non-linear response. (2) Methods: To characterize the influence of platelets on the network level, a stress amplitude sweep test (LAOStress) was applied to clots from native plasma with five platelet concentrations. Five species were used to validate the protocol (human, cow, pig, rat, horse). By Lissajous plots the oscillation cycle for each stress level was analyzed. (3) Results: Cyclic stress loading generates a characteristic strain response that scales with the platelet quantity at low stress, and that is independent from the platelet count at high shear stress. This general behavior is valid in the animal models except cow. Here, the specific fibrinogen chemistry induces a stiffer network and a variant high stress response. (4) Conclusions: The protocol provides several thresholds to connect the softening and stiffening behavior of clots with the applied shear stress. This points to the reversible part of deformation, and thus opens a new route to describe a blood clot’s phenotype.