The discovery of half-metallic Dirac cones in metal–organic frameworks (MOFs) opens up new prospects for future spintronic devices. Although this unique feature has been demonstrated in several theoretically designed MOFs, none of these have been synthesized. Therefore, the exploration of half-metallic Dirac features in experimentally synthesized MOFs is extremely significant. In this study, via density functional theory, we investigate two recently synthesized two-dimensional (2D) metal-semiquinoid frameworks (V-SF and Ti-SF) as novel Dirac materials with ultrahigh Fermi velocities (up to 3.74 × 105 m s−1), which are comparable to that of graphene. Notably, Ti-SF exhibits a Dirac dispersion in only one spin channel, while it is semiconducting with a bandgap of 1.67 eV in the other spin channel. This is the first report of a half-metallic Dirac feature in experimentally synthesized MOFs. Furthermore, we adopted a molecular orbital model to analyse the magnetism of MOFs with D3 symmetry. The model accurately describes the magnetism of 3d transition metal-semiquinoid frameworks, and we expected it to instruct further research focused on magnetic complexes.