Natural selection has tuned many flying and swimming animals to share the same narrow design space for high power efficiency, e.g., their dimensionless Strouhal numbers St that relate flapping frequency and amplitude and forward speed fall within the range of 0.2 < St < 0.4 for peak propulsive efficiency. It is rather challenging to achieve both comparably fast-speed and high-efficient soft swimmers to marine animals due to the naturally selected narrow design space and soft body compliance. Here, bioinspired by the flapping motion in swimming animals, we report leveraging snapping instabilities for soft flapping-wing swimmers with comparable high performance to biological counterparts. The lightweight, butterfly stroke-like soft swimmer (2.8 g) demonstrates a record-high speed of 3.74 body length/s (4.8 times faster than the reported fastest flapping soft swimmer), high power efficiency (0.2 < St = 0.25 < 0.4), low energy consumption cost, and high maneuverability (a high turning speed of 157°/s).