Progressive and intermittent cutting scheme has been found useful for heterogeneous and difficult-to-machine materials such as fibre-reinforced polymer composites. Though a controlled eccentricity to the rotation of grinding wheel is projected as one of the simplest methodologies to achieve such a unique cutting scheme, the major apprehension is the influence of eccentricity on grinding dynamics. This research aims to understand the influence of eccentricity on the grinding performance and surface integrity of carbon fibre reinforced polymer composites (CFRPs) and to establish a guideline for the selection of eccentricity for a progressive-intermittent cutting scheme. Surface/sub-surface level defect estimations via SEM and X-ray computed tomography, analysis of Raman spectra for residual stress patterns, 3D surface topography assessment on ground surface, etc., presented in this work may provide useful benchmarks for the selection of grinding strategies and processing conditions for machining unfriendly materials like CFRPs.