Microsurgical manipulations are key experimental techniques in life science research, particularly in embryology. These techniques are most often performed manually by highly skilled scientists, posing limitations on speed, precision, and reproducibility. Here we introduce a fully automated robotic microsurgery platform that generates explants of specific tail tissue from growing zebrafish embryos, a popular model organism for vertebrate development. Our work leverages both classical and deep learning-based image-processing techniques to perform robotic micromanipulation on biological specimens. Using two example experimental cases as proof of concept, we show that our automated platform is more precise, accurate, and efficient than teleoperated and manual microsurgery conducted by experienced scientists. Moreover, we demonstrate the usefulness of our platform for inexperienced experimentalists, supporting an important role for robotic microsurgery in broadening the use of such techniques in experimental research.