Traditional machining techniques pose significant drawbacks when applied to ceramics due to the material's inherent brittleness. Specialized laser machining has been known to solve these issues through higher precision and micrometer-scale feature control. In this study, a picosecond fiber laser has been proposed as a near-net shaping material removal system for different engineering applications of industrial grade alumina ceramics with a variety of thicknesses and feature dimensions. This article particularly focuses on optimizing picosecond laser processing parameters (i.e., wobble amplitude, wobble frequency, wobble pitch, linear speed and number of passes) that were implemented to obtain ablated, deep, smooth and defect-free designed cut geometries (i.e., kerf taper and cut depth) with a high degree of precision. The surface roughness was assessed to determine the quality of the cuts. The optimal process parameters between the quality and material removal rate were introduced. Using a circular wobble laser pattern, it was determined that a greater cut depth can be achieved at lower linear speeds and wobble frequencies due to the higher linear energy density. It has also been found that the kerf taper is dependent on the cut depth and wobble amplitude, where the measured cuts follow the geometric relation between these parameters accurately. In addition, a maximum material removal rate of ~ 10 mm3/min was achieved to make a desired ablated cut profile in the alumina ceramic tiles as thick as 2.54 mm (0.1 in).