Arc splitting is one of the most important processes in accomplishing a power interruption by multiplying the number of voltage drops. During arc-plate interaction, the arc roots erode and vaporize the metals which significantly alters the gas composition and plasma properties, such as the radiation absorption coefficient. In this work, we perform a 3D computational study of arc splitting in a circuit breaker. In order for the study to be systematic, the metal vaporization, species transport, and radiative heat transfer are integrated into the magnetohydrodynamics modeling with some special considerations. Firstly, the simulation considers the ferromagnetic effect of steel plates. Secondly, the metal-vapor-enhanced radiation is numerically implemented by the discrete ordinate method with consideration given to the banded radiation spectrum. Thirdly, the simulation model incorporates a near-electrode layer to implement the voltage drop and imposes additional heat flux on the arc spots. The simulation results show that the metal vaporization not only influences the arc dynamics (via Stefan flow) but also enhances the local radiation intensity. Besides, due to the ferromagnetic effect, the magnetic field increases dramatically during arc splitting. However, the self-induced magnetic force has quite a different influence on the motion of sub-arcs, which prevents even and concurrent arc splitting. This simulation reveals that the magnetic-field-induced uneven splitting can be compensated by the enhanced pressure wave or externally applied transversal magnetic field. This study is expected to explore more applications in simulating arc interruption and improve the design of highly-efficient circuit breakers.