Modern manufacturing industries make use of laser drilling of metals and alloys as a tool for production of holes of different sizes and shapes. During recent years laser drilling of aerospace nickel super alloys is mostly done with the help of laser beam machining. Trepan drilling process is an attractive choice in high value manufacturing industries. But it is very complicated for 50-watt average power machine to achieve high-quality cutting/drilling of the metal sheet upto 2 mm thickness. A rare input parameter of sawing angle acts as an important role in top and bottom diameter deviation in drilling Monel k-500 alloy sheet of 0.7 mm thickness in low power fiber laser beam machining. The present study deals with the effect of sawing angle with other process parameters like average power, duty cycle, pulse repetition rate and scanning speed on the diameter deviation for a Monel metal sheet. Optimization of controllable process parameters helps to obtain required diameter deviation which is validated in the proposed model. For prediction of the effect of independent process parameters on laser cut quality, a model has been developed with the help of regression analysis. Teaching learning-based algorithm method has been used to obtain the minimum diameter deviation at top and bottom sides.