To investigate vibration transmission and mitigation in a phononic crystal embedded rail track under transient wheel–rail impact, full-scale drop-wheel tests were conducted in comparison with a conventional fastened track. Three conditions were examined: 15 mm unloaded, 15 mm fully loaded, and 25 mm unloaded. Vertical accelerations were recorded simultaneously at the rail, track slab, and foundation. Six time–frequency analysis methods were compared in terms of energy concentration and consistency with vibration decay. Wavelet synchro squeezing transform (WSST) was selected to examine the time–frequency evolution of the impact response, while one-third-octave vibration levels were used to evaluate the mitigation effect. WSST achieved the highest overall evaluation index among the six methods, at 0.52192. In the phononic crystal embedded rail track, the vibration response decreased progressively from the rail to the track slab and foundation, with the foundation response concentrated mainly within 20–80 Hz. Compared with the conventional fastened track, its overall vibration levels under the three conditions were lower by 29.5, 15.1, and 3.9 dB within 1–80 Hz, and by 28.8, 14.4, and 3.4 dB within 4–200 Hz, respectively. WSST characterizes the dominant frequency ridges and their decay following drop-wheel impact, providing a basis for a more detailed evaluation of track vibration mitigation under transient impact.