We study downlink multi-group multicast (MGM) transmission in overloaded millimeter-wave (mmWave) systems, where the number of users exceeds the number of transmit antennas. We first show that, under realistic line-of-sight (LoS)-dominant user geometries, the conventional single-slot MGM scheme suffers from a fundamental collapse of the max-min fairness degrees of freedom (MMF-DoF), regardless of beamforming optimization. Although this collapse can in principle be avoided via aggressive time-division scheduling, it requires excessive time sharing and results in severe throughput loss in overloaded regimes. To address this limitation, we propose a CSIT-free multi-group multicast framework (CF-MGM) that does not rely on instantaneous channel state information at the transmitter (CSIT) and is based on a deterministic multi-slot transmission structure. By exploiting structured precoding and receiver-side combining across multiple slots, the proposed framework eliminates inter-group interference by construction. We show that CF-MGM guarantees a strictly positive MMF-DoF in overloaded LoS mmWave systems, in sharp contrast to the DoF collapse of conventional single-slot MGM. Simulation results demonstrate that CF-MGM significantly outperforms state-of-the-art CSIT-based MGM schemes while substantially reducing signaling overhead.