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Biological tissues possess high stretchability and nonlinear mechanical response owing to their wavy and crimped microstructure. The metamaterials exhibit unusual physical and mechanical properties, dominated by the configuration of artificial periodic microstructures. However, the development of bio-inspired designs and three-dimensional (3D) soft metamaterials that can achieve a variety of unusual mechanical properties remains challenging. Here, we reported a class of 3D horseshoe-shaped soft network metamaterials with tunable nonlinear mechanical response and tension-torsion coupling effect. Based on the 3D horseshoe-shaped microstructure and octahedron lattice arrangement, the designed 3D soft network metamaterials can exhibit J-shaped stress-strain curve and large angle of torsion with large levels of deformation under tension. The mechanical properties of the 3D soft network metamaterials in different characteristic directions are investigated, where a negative Poisson's ratio appears. Furthermore, the extended design that the 3D horseshoe-shaped microstructures are replaced by the semi-elliptic and quarter-arc-straight joint microstructures can tune a wide range of desired J-shaped stress-strain curves. Thus, the multi-unusual mechanical properties provide potential uses in multi-functional metamaterials and flexible bio-integrated devices. [ABSTRACT FROM AUTHOR]