Current research focuses on optimizing various quality characteristics for kerf geometry generated through laser cutting of Coir fibre/carbon fibre/epoxy resin hybrid composite adjacent to straight cut profile employing pulsed CO2 laser system. The Kerf taper (KT) and the Surface roughness (SR) are the main quality parameters discussed. Dependent on significant process parameters, namely gas pressure, cutting speed, pulse frequency and pulse width predictive models were developed. In accordance with Taguchi's L9 orthogonal array (OA), the cutting trials are designed. Process-parametric optimization was performed using Response Surface Methodology (RSM). Furthermore, experiments were performed to obtain experimental data for the analysis of cut quality features. The impact of the input variables on the response characteristics is also explored. The morphological characterizations have been performed to analysis the effect of machining-variables and cut-quality for the top and bottom kerf widths with various laser cutting variables in the pulse laser-cutting of Coir-fibre/carbon-fibre/epoxy-resin hybrid composite. For SR and KT, the developed second order surface response model was found very successful. The optimal levels of cutting variables for KT are established at Gas pressure-6 N/mm2, pulse width-2.04 ms, cutting speed-8.01 mm/s, pulse frequency-15 Hz, for sample A1, Gas pressure-5.47 N/mm2, pulse width-2.5 ms, cutting speed-8.81 mm/s, pulse frequency-8.43 Hz, for sample A2, Gas pressure-3.85 N/mm2, pulse width-1.5 ms, cutting speed-9.06 mm/s, pulse frequency-5 Hz, for sample A3 additionally for SR Gas pressure-2 N/mm2, pulse width-1.5 ms, cutting speed-7 mm/s, pulse frequency-5 Hz, for sample A1, Gaspressure-2.36 N/mm2, pulse width-1.5 ms, cutting speed-7 mm/s, pulse frequency-15 Hz, for sample A2, Gaspressure-6 N/mm2, pulse width-1.5 ms, cutting speed-11 mm/s, pulse frequency-8.73 Hz, for sample A3. Regression results and linear and square impact of laser cutting variables have been revealed to be important to validate the model.