Ti and Mg alloys, which have thermodynamically immiscible main components, have been chemically joined in previous work using a third element with high affinity for both elements. However, this strategy is challenging in precisely controlling brittle intermetallic compounds formed at a joint interface. In this study, we mechanically joined pure Ti and pure Mg without brittle layers by forming bicontinuous microstructure, 3D entanglement of immiscible phases, at the joint interface. We butt-joined pure Mg and Ti–Cu alloy interlayer, which we pre-diffusion bonded to the pure Ti and heated at 813 K and 20 MPa for 5 min. At the joint interface, Cu and Mg eutectic melted, which induced liquid metal dealloying of the interlayer. The entire Ti–Cu interlayer is dealloyed, and a byproduct (Mg–Cu phase) is removed by pressurization during melting. These brittle layer removal processes left only α-Ti/Mg–Cu phase bicontinuous microstructure at the joint interface, improving the joint strength. Ti/Mg joints fractured at the Mg base metal at ca. 90 MPa by tensile tests. The findings of this study provide the basis for achieving immiscible alloy joining, for which effective joining methods have not yet been established.