Here, a concept for merging intrinsically stretchable materials with engineered stretchability by kirigami-patterning on a component level is shown to yield high-power biodegradable batteries with reversible elasticity up to 35% when stretched uniaxially and 20% for biaxial extension. Using a combination of molybdenum metal foils, a molybdenum trioxide paste, and magnesium metal foils as electrode materials, a peak power output of 196 µW/cm² and an energy density of 1.72 mWh/cm² is achieved.