<p>Fluids with internal microstructure are ubiquitous in biological, industrial, and geophysical settings, yet their flow behaviour remains far from fully understood. Recent works have demonstrated that the interplay between fluid elasticity and flow shear drives instabilities and wave propagation in canonical setups, yet the dynamics of viscoelastic mixing layers remain largely unexplored. Here we show that waves develop in a time-decaying viscoelastic mixing layer, causing the mean flow to yo-yo, periodically reversing direction in sharp contrast to the monotonic, Newtonian decay. Direct numerical simulations and energetic analysis reveal that these reversals are driven by the elastic microstructure injecting energy into the fluid while being reoriented by the mean shear. A reduced model admits linear wave solutions with nonlinear dispersion, accurately predicting the reversal period and the parameter range where yo-yoing occurs. As mixing layers are prototypical free shear flows, our findings offer a framework for understanding anomalous dynamics in unsteady viscoelastic flows, with implications for microfluidic mixing.</p>