Cellular materials are usually exploited in industrial applications as energy absorbers in which the impact is mitigated by their large deformation. Nowadays, additive manufacturing technologies allow the designing of new complex cellular materials capable of exhibiting advanced mechanical properties. An increase in structure crashworthiness is observed introducing a coupled twisting-axial deformation. The base TPMS structures are twisted along a preferential axis to couple both deformations. The energy absorption characteristics have been investigated under quasi-static and dynamic compression loadings. A Split Hopkinson bar is set up to measure the axial loading and torque during high strain rate compression. The experimental results show an enhancement of crashworthiness performances once the structure is free to be twisted. Therefore, the study highlights a new design strategy aimed to improve impact absorption of cellular materials.