The design of intersecting nodes in high-rise oblique mesh structures is a critical issue. The existing research on the intersecting nodes of oblique meshes mainly focuses on plane intersecting nodes and monotonic axial compression loads. The plane intersecting nodes cannot consider the contribution of the node’s out-of-plane angle and floor beam to the node’s out-of-plane stiffness in actual structures. In this paper, numerical analysis using ABAQUS was conducted to investigate the mechanical performance of space intersecting nodes of oblique meshes (OMSIN) under cyclic axial tension and compression loads, to provide a reference for the engineering application of oblique mesh structures in seismic regions. Six parameters were considered: the space intersecting angle, the plane angle symmetry coefficient, the plane intersecting angle, the out-of-plane constraint restraint, the steel content of the cross-section, and the concrete strength. The study showed that changes in the thickness of the steel tube wall are unfavourable for the uniform transmission of stress. Increasing the space intersecting angle significantly weakened the seismic performance, and the space angle affects the failure mode of the node. Asymmetric arrangements of the upper and lower plane angles caused nonlinear development of out-of-plane. The ultimate load and overall compressive stiffness of the specimen were positively correlated with the plane angle, and vertical constraints should be applied to the node position of components with plane angles greater than or equal to 70°. The out-of-plane constraint was a key factor affecting the seismic performance of the node, and it was proportional to the ultimate load of the component. In structural design, if the aim is to improve the mechanical performance of the component by increasing the steel content, more enormous out-of-plane constraints should be set to control plane external displacement strictly. The concrete strength is proportional to the ultimate axial load and axial stiffness, and its influence on the mechanical performance in the axial tension direction is not significant. Finally, a dimensionless skeleton curve model of the node was established. The existing formula for the bearing capacity of CFST columns was fitted to obtain the calculation formula for the axial yield and ultimate load of the OMSIN under cyclic loads.