Machining composite to achieve the desired surface and sub-surface condition, whether through conventional or non-conventional techniques, presents persistent challenges due to their anisotropic thermal characteristics. These challenges escalate when dealing with ceramic matrix composites (CMC) due to their high melting and boiling temperature. This study investigates the surface and sub-surface characteristics of SiC-Al2O3 CMC laser-cut components, produced using a 2 kW quasi-continuous wave laser. The influence of laser parameters such as focal position, cutting speed, number of cutting passes, average power, and assist gas type on surface and sub-surface characteristics have been investigated in detail. The laser cut samples were analysed using white light interferometer, Scanning Electron Microscopy (SEM), Energy Dispersive X-ray Spectroscopy (EDX) and 3D X-ray Computer Tomography (XCT) for both surface and sub-surface characteristics. The effect of laser process parameters on the surface composition, surface topology, and sub-surface thermal defects have been studied in detail. The results revealed that multi-pass cutting (16 pass) can be used to achieve lower thermal affected zone (~200 µm) and reduced surface roughness with an overall cutting speed of 625 mm/min. No delamination was observed with multi-pass cutting. Nitrogen was found to be the most suitable assist gas, as it prevented oxide layer formation across the laser cut SiC-Al2O3 CMC surface.