TA1 titanium bipolar plates for hydrogen fuel cells are prone to plastic instability phenomena such as wrinkling during the stamping process, which adversely affects the forming quality. This study applies an ultrasonic-vibration energy field, aligned with the direction of stretching, in a plate diagonal tensile testing scenario based on the Blaha effect. The impact of varying thicknesses and vibration amplitudes on the anti-wrinkling performance of TA1 titanium sheets is investigated. Through a combined analysis of load–displacement curves and wrinkle height measurements using a super-depth-of-field microscope, by examining the forming load, the onset of wrinkling, and the wrinkle height at buckling locations, this study explores the deformation behavior of the thin sheet and the wrinkle suppression mechanism under the coupled effects of the ultrasonic-vibration field and scale. The results show that as the thickness decreases, the anti-wrinkling ability of the TA1 titanium sheet diminishes. The ultrasonic-vibration energy field reduces the yield stress and flow stress of the material, promoting wrinkling during the elastic deformation stage. Moreover, the 0.075 mm thick TA1 titanium sheet experiences local secondary wrinkling during the plastic deformation stage. Additionally, the ultrasonic-vibration energy field effectively reduces the forming load of the sheet and suppresses wrinkling within a certain range of amplitudes. These findings provide experimental evidence for the ultrasonic-vibration-assisted stamping process of titanium bipolar plates.