Intercalated layered materials offer distinctive properties and serve as precursors for important two-dimensional (2D) materials. However, intercalation of non-van der Waals structures, which can expand the family of 2D materials, is difficult. We report a structural editing protocol for layered carbides (MAX phases) and their 2D derivatives (MXenes). Gap-opening and species-intercalating stages were respectively mediated by chemical scissors and intercalants, which created a large family of MAX phases with unconventional elements and structures, as well as MXenes with versatile terminals. The removal of terminals in MXenes with metal scissors and then the stitching of 2D carbide nanosheets with atom intercalation leads to the reconstruction of MAX phases and a family of metal-intercalated 2D carbides, both of which may drive advances in fields ranging from energy to printed electronics.