A magnetic stirrer, an omnipresent device in the laboratory, generates a spinning magnetic dipolelike field that drives in a contactless manner the rotation of a ferromagnetic bead on top of it. We investigate here the surprisingly complex dynamics displayed by the spinning magnetic bead emerging from its dissipatively driven, coupled translation and rotation. A particularly stunning and counterintuitive phenomenon is the sudden inversion of the bead's rotational direction, from corotation to counterrotation, acting seemingly against the driving field, when the stirrer's frequency surpasses a critical value. The bead counterrotation effect, experimentally described by Chau et al. [J. Magn. Magn. Mater. 476, 376 (2019)JMMMDC0304-885310.1016/j.jmmm.2018.12.073], is here comprehensively studied, with numerical simulations and a theoretical approach complementing experimental observations.