The central engine of gamma-ray bursts (GRBs) is believed to be a hot and dense disk with hyperaccretion onto a few solar-mass black hole. We investigate where the magnetorotational instability (MRI) actively operates in the hyperaccretion disk, which can cause angular momentum transport in the disk. The inner region of hyperaccretion disks can be neutrino opaque, and the energy and momentum transport by neutrinos could affect the growth of the MRI significantly. Assuming reasonable disk models and a weak magnetic field B 10¹⁴ G, it is found that the MRI is strongly suppressed by the neutrino viscosity in the inner region of hyperaccretion disks. On the other hand, the MRI can drive active magnetohydrodynamic turbulence in the outer neutrino-transparent region regardless of the field strength. This suggests that the baryonic matter is accumulated into the inner dead zone, where the MRI grows inactively and the angular momentum transport is inefficient. When the dead zone gains a large amount of mass and becomes gravitationally unstable, intense mass accretion onto the central black hole would occur episodically through the gravitational torque. This process can be a physical mechanism of the short-term variability in the prompt emission of GRBs. Finally, the origin of flaring activities in the X-ray afterglow is predicted in the context of our episodic accretion scenario.