In a global context, where the construction industry is a major source of CO2 emissions and resource use, is dependent on concrete and its risks, and lags behind in digitalization, a clear need arises to direct architecture towards more practical, efficient, and sustainable practices. This research introduces an alternative technique for building timber space structures, aiming to expand its applications in areas with limited access to advanced technologies such as CNCs with more than five axes and industrial robotic arms. This involves reconfiguring economic and ecological constraints to maximize the structural and architectural advantages of these systems. The method develops a parametric tool that integrates computational design and manufacturing based on two-axis laser cutting for shells with segmented hexagonal plywood plates. It uses a modified ‘half-lap joint’ mechanical joint, also made of plywood and without additional fasteners, ensuring a precise and robust connection. The results demonstrate the compatibility of the geometry with two-axis CNC machines, which simplifies manufacturing and reduces the cuts required, thus increasing economic efficiency. The prototype, with a span of 1.5 m and composed of 63 plywood panels and 163 connectors, each 6 mm thick, supported a point load of 0.8 kN with a maximum displacement of 5 mm, weighing 15.1 kg. Assembly and disassembly, carried out by two students, took 5 h and 1.45 h, respectively, highlighting the practicality and accessibility of the method. In conclusion, the technique for building timber shells based on two-axis CNC is feasible and effective, proven by practical experimentation and finite element analysis.