Black hole X-ray binaries (BHXRBs) display a wide range of variability phenomena, from long duration spectral state changes to short-term broadband variability and quasi-periodic oscillations (QPOs). A particularly puzzling aspect is the production of QPOs, which -- if properly understood -- could be used as a powerful diagnostic tool of black hole accretion and evolution. In this work we analyse a high resolution three-dimensional general relativistic magnetohydrodynamic simulation of a geometrically thin accretion disk which is tilted by $65^{\circ}$ with respect to the black hole spin axis. We find that the Lense-Thirring torque from the rapidly spinning 10 $M_\odot$ black hole causes several sub-disks to tear off within $\sim 10-20$ gra...