While bionic designs show significant promise in improving the hydraulic performance of fluid machinery, achieving these benefits in engineering applications requires meticulous design and optimization. Inspired by the biomimetic features of humpback whale and Atlantic bluefin tuna, we proposed a bio-inspired design approach to collaboratively optimize both the impeller and diffuser of slanted axial-flow pumps, incorporating leading-edge (LE) tubercles and trailing-edge (TE) serrations. To improve the overall hydraulic performance, several geometric design variables of LE tubercles and TE serrations were considered using a surrogate model for multi-objective optimization. In contrast with the baseline case without bionic design, LE tubercles and TE serrations significantly improved the hydraulic performance under overload conditions, increasing the head and efficiency by up to 7.59% and 3.47%, respectively. In particular, we found that the wavy shape of the LE tubercles promoted a more gradual pressure distribution around the impeller, reducing the formation of low-pressure regions near the suction side that lead to cavitation and decreasing the cavitation bubble volume by up to 19.40%. TE serrations were shown to minimize flow separations and vortex shedding, thereby stabilizing vortex patterns and reducing transverse flow between the serrations. Optimizing the TE serrations resulted in a 16.38% decrease in discharge passage loss compared to the baseline. Extending the TE serration section helped to reduce flow deviation in the outlet passage, decreasing the deviation coefficient by up to 17.46% under rated condition. An experimental comparison validated the advantage of the bio-inspired design approach.