Green sea turtles (Chelonia mydas) can swim up to 50 km per day while only consuming seagrass or microalgae. How the animal accomplishes this vast journey on such low energy intake points to the effectiveness of their swimming technique and is a testament to the power of evolution. Understanding the green sea turtle's ability to accomplish these journeys requires insight into their propulsive strategies. Conducting animal testing to uncover their propulsive strategies brings significant challenges: firstly, the ethical issues of conducting experiments on an endangered animal, and secondly, the animal may not even swim with its regular routine during the experiments. In this work, we develop a new soft-robotic sea turtle that reproduces the real animal's form and function to provide biomechanical insights without the need for invasive experimentation. We found that the green sea turtle may only produce propulsion for approximately 30% of the limb beat cycle, with the remaining 70% exploiting a power-preserving low-drag glide. Due to the animal's large mass and relatively low drag coefficient, losses in swim speed are minimal during the gliding stage. These findings may lead to the creation of a new generation of robotic systems for ocean exploration that use an optimised derivative of the sea turtle propulsive strategy.