Jumping on water is a unique locomotion mode found in semi-aquatic arthropods, such as water striders. To reproduce this feat in a surface tension-dominant jumping robot, we elucidated the hydrodynamics involved and applied them to develop a bio-inspired impulsive mechanism that maximizes momentum transfer to water. We found that water striders rotate the curved tips of their legs inward at a relatively low descending velocity with a force just below that required to break the water surface (144 millinewtons/meter). We built a 68-milligram at-scale jumping robotic insect and verified that it jumps on water with maximum momentum transfer. The results suggest an understanding of the hydrodynamic phenomena used by semi-aquatic arthropods during water jumping and prescribe a method for reproducing these capabilities in artificial systems.