The design of damage-tolerant aeronautical composite structures often involves thin-walled components that are susceptible to in-plane mixed-mode fracture. Unlike with metals, this process is complicated by the composites anisotropy and the lack of standardized procedures for predicting failure in notched, holed or cracked composites under mixed-mode loading. This study introduces a novel Modified Arcan Fixture (MAF) for testing Compact Tension Shear (CTS) specimens of carbon fibre woven reinforced polymer composite. Digital Image Correlation (DIC) was used to capture strain fields and calculate Stress Intensity Factors (SIFs), which were then compared to analytical predictions for different mode combinations and notch lengths. R-curves were generated for specimens exhibiting self-similar crack propagation. The results revealed that failure modes were dominated by tensile cracking in Mode I and compressive cracking in Mode II, indicating that a single-parameter fracture criterion inadequate for the failure description. A theoretical model that incorporates both tensile and compressive cracking is proposed, which can accurately predict the complete mixed-mode fracture envelope. Furthermore, Scanning Electron Microscopy (SEM) and X-ray micro-tomography were used to elucidate the mechanisms of surface failure and the morphology of internal damage.