Nowadays, composite sandwich tubes are extensively utilized in the civil and aerospace industries due to their superior strength-to-weight mechanical properties. Origami-based core offers a large enhancement of the mechanical properties, yet little study research focuses on the effect of various foldcore configurations on the transverse mechanical properties of sandwich tubes, necessitating the design method for applications. This study introduces an innovative approach by incorporating origami into the composite sandwich core to enhance the transverse energy absorption capacity. The quasi-static transverse mechanical properties of carbon fibre-reinforced polymer (CFRP) sandwich tubes with foldcores are studied under three-point bending-like local compression and transverse structural compression. A systematic geometric design framework and numerical modelling technique are provided. By integrating finite element analysis and experiments, the research investigates the effects of various origami foldcore configurations and geometric parameters on transverse energy absorption capacity. The experiment setup is provided by sandwich tubular specimens with a full-diamond configuration as the foldcore. The cylindrical tubes (foldcore) of the sandwich structures were manufactured using four plies [0°]4 of T700 (T300) woven CFRP with the hot press moulding (vacuum bag using female and male moulds) technique respectively. Then, the parametric study and damage mode analysis of eight different foldcore patterns (axial Miura, circumferential Miura, diamond, Kresling, and their curved-creased counterparts) were studied. The results showed the superior energy absorption performance of the sandwich tube with Miura-pattern foldcore over the origami-pattern counterparts, nested tube, and traditional honeycomb sandwich tube with CFRP or aluminium-made cores. Therefore, the structural parameters optimisation of the Miura pattern tube was carried out by the Response Surface method (RSM) and a design strategy for increasing the energy absorption capacity was found. The findings offer guidance for designing high-specific energy absorption tubular structures for future advanced engineering applications.