The effect of a transient magnetic field on right-hand circularly polarized (RHCP) laser light propagation in overcritical-density plasma is investigated. When the electron gyrofrequency is larger than the wave frequency, RHCP light can propagate along the external magnetic field in an overcritical density plasma without resonance or cutoff. However, when the magnetic field falls to below the cyclotron resonance point, the propagating laser pulse will be truncated and the local plasma electrons resonantly heated. Particle-in-cell simulation shows that when applied to a thin slab, the process can produce intense two-cycle light pulses as well as long-lasting self-magnetic fields.