In non-traditional machining, micro-abrasive jet machining (MAJM) is a cost-effective machining process. MAJM has been used for fabricating electronic devices and microfluidic channels. This work has made an effort to utilize MAJM for glass. A new design and fabrication of the Laval type of nozzle have been proposed to improve machining accuracy. A nozzle is conceived to ensure specific characteristics of the mixture (compressed air and abrasive particles) pass through it. The abrasive particle force is converted to kinetic energy, increasing the mixture’s velocity. The cross-sectional area of the nozzle can be circular, rectangular, square, or oval. A circular cross-sectional nozzle has been developed for high velocity, precise etching, and patterning on difficult-to-machine materials such as steel alloys. A circular cross-sectional micro-nozzle with a large aspect ratio is proposed, and the flow characteristics and cutting performance are examined precisely by the experiment. Efforts are being made to make machining processes sustainable, productive, and efficient. Here, the Taguchi-grey relational analysis integration approach has been used to analyze the machining parameters such as air pressure, stand-off distance, and abrasive mesh size (AMS). The top hole diameter, bottom hole diameter, material removal rate, and radial overcut are the response variables in this investigation. Analysis of variance (ANOVA) results showed that the AMS was the most efficient parameter, which followed the processing condition on the total input of the multi-purpose function. The reported optimized process parameters are air pressure of 8 bar, stand-off distance of 2 mm, and AMS mix (50%+100%) micron, which significantly affects the top and bottom micro-hole diameters.