Snap-through, a rapid transition of a system from an equilibrium state to a nonadjacent equilibrium state, is a valuable design element of soft devices for converting a monolithic stimulus into systematic responses with impulsive motions. A common way to benefit from snap-through is to embody it within structures and materials, such as bistable structures. Torque-reversal mechanisms discovered in nature, which harness snap-through instability via muscular forces, may have comparative advantages. However, the current intricacy of artificial torque-reversal mechanisms, which require sophisticated kinematics/kinetics, constrains design possibilities for soft joints and devices. Here, we harnessed hyperelasticity to implement a torque-reversal mechanism in a soft joint, generating repetitive cilia-like beating motions through an embedded tendon. The developed hyperelastic torque-reversal mechanism (HeTRM) exhibits transient bistability under a specific compressive displacement/force threshold, with snap-through occurring at the point where the transience ends. To validate the effectiveness of this design principle, we explored the functionalities of HeTRM in energy storage and release, dual modes for impulsive and continuous motion, mechanical fuse, and rapid three-dimensional motions, through proof-of-concept soft machines. We expect that this design principle provides insight into incorporating snap-through behavior in soft machines and may aid in understanding the relationship between torque-reversal mechanisms and bistability.