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ABSTRACT Luminous active galactic nuclei and X-ray binaries often contain geometrically thin, radiatively cooled accretion discs. According to theory, these are – in many cases – initially highly misaligned with the black hole equator. In this work, we present the first general relativistic magnetohydrodynamic simulations of very thin (h/r ∼ 0.015–0.05) accretion discs around rapidly spinning (a ∼ 0.9) black holes and tilted by 45°–65°. We show that the inner regions of the discs with h/r ≲ 0.03 align with the black hole equator, though out to smaller radii than predicted by analytic work. The inner aligned and outer misaligned disc regions are separated by a sharp break in tilt angle accompanied by a sharp drop in density. We find that frame dragging by the spinning black hole overpowers the disc viscosity, which is self-consistently produced by magnetized turbulence, tearing the disc apart and forming a rapidly precessing inner sub-disc surrounded by a slowly precessing outer sub-disc. We find that the system produces a pair of relativistic jets for all initial tilt values. At small distances, the black hole launched jets precess rapidly together with the inner sub-disc, whereas at large distances they partially align with the outer sub-disc and precess more slowly. If the tearing radius can be modeled accurately in future work, emission model independent measurements of black hole spin based on precession-driven quasi-periodic oscillations may become possible.