Carbon-fiber-reinforced polymer (CFRP) tendons have become a viable alternative to steel cables in cable roof structures owing to their high tensile strength, low weight, and resistance to corrosion. However, the effective anchoring of CFRP tendons is a challenge because of their poor transverse mechanical properties. Therefore, the mechanical properties of CFRP tendons and a tendon–wedge assembly under transverse compression were investigated by simulating the force environment of the CFRP tendon inside an integrated-wedge anchorage. The deformation of and local damage to CFRP tendons under transverse compression were explored using load–strain curves and full-field strain measured using digital image correlation. The experimental and numerical results show that large-diameter CFRP tendons with a length in the range of 90–110 mm had better cross-sectional deformation resistance and more stable transverse mechanical properties. Longer CFRP tendons with larger diameters have lower contact compressive stress and local maximal shear stress under the same transverse compressive load. Based on the analysis of the experimental and numerical results, we propose design suggestions for tendon size selection and integrated-wedge design details, such as the manufacturing materials of the wedge, the radius through the gap of the wedge, and the radial difference of the groove, to improve the anchoring properties and efficiency of the integrated-wedge anchorage.