There is a growing need for vertical take-off and landing vehicles, including drones, which are safe to use and can adapt to collisions. The risks of damage by collision, to humans, obstacles in the environment, and drones themselves, are significant. This has prompted a search into nature for a highly resilient structure that can inform a design of propellers to reduce those risks and enhance safety. Inspired by the flexibility and resilience of dragonfly wings, we propose a novel design for a biomimetic drone propeller called Tombo propeller. Here, we report on the design and fabrication process of this biomimetic propeller that can accommodate collisions and recover quickly, while maintaining sufficient thrust force to hover and fly. We describe the development of an aerodynamic model and experiments conducted to investigate performance characteristics for various configurations of the propeller morphology, and related properties, such as generated thrust force, thrust force deviation, collision force, recovery time, lift-to-drag ratio, and noise. Finally, we design and showcase a control strategy for a drone equipped with Tombo propellers that collides in mid-air with an obstacle and recovers from collision continuing flying. The results show that the maximum collision force generated by the proposed Tombo propeller is less than two-thirds that of a traditional rigid propeller, which suggests the concrete possibility to employ deformable propellers for drones flying in a cluttered environment. This research can contribute to morphological design of flying vehicles for agile and resilient performance.