Using resonant soft-x-ray scattering as a function of both temperature and magnetic field, we reveal a large number of almost degenerate magnetic orders in SrCo6O11. The Ising-like spins in this frustrated material in fact exhibit a so-called magnetic devil's staircase. It is demonstrated how a magnetic field induces transitions between different microscopic spin configurations, which is responsible for the magnetoresistance of SrCo6O11. This material therefore constitutes a unique combination of a magnetic devil's staircase and spin-valve effects, yielding a novel type of magnetoresistance system.