The machining of ceramic materials is challenging and often impossible to realize with conventional machining tools. In various manufacturing applications, rotary ultrasonic milling (RUM) shows strengths, in particular for the development of high-quality micro-features in ceramic materials. The main variables that influence the performance and price of the product are surface roughness, edge chipping (EC), and material removal rate (MRR) during the processing of ceramics. RUM has been considered in this research for the milling of micro-pockets in bioceramic alumina (Al2O3). Response surface methodology in the context of a central composite design (CCD) is being used to plan the experiments. The impacts of important RUM input parameters concerning cutting speed, feed rate, depth of cut, frequency, and amplitude have been explored on the surface roughness in terms of arithmetic mean value (Ra), the EC, and the MRR of the machined pockets. The main effect and the interaction effect of the implemented RUM parameters show that by providing a lower feed rate and cutting depth levels and elevated frequency and cutting speed, the Ra and the EC can be minimized. At greater levels of feed rate and cutting depth, higher MRR can be obtained. The influence of RUM input parameters on the surface morphology was also recorded and analyzed using scanning electron microscopic (SEM) images. The study of the energy dispersive spectroscopy (EDS) shows that there is no modification in the alumina bioceramic material. Additionally, a multi-response optimization method has been applied by employing a desirability approach with the core objectives of minimizing the EC and Ra and maximizing the MRR of the milled pockets. The obtained experimental values for Ra, EC, and MRR at an optimized parametric setting were 0.301 µm, 12.45 µm, and 0.873 mm3/min respectively with a combined desirability index value of 0.73.