A protoplanetary disk (PPD) typically forms a dead zone near its midplane at a distance of a few astronomical units from the central protostar. Accretion through such a magnetically layered disk can be intrinsically unstable and has been associated with episodic outbursts in young stellar objects. We present the first investigation into the effects of a low-metallicity environment on the structure of the dead zone, as well as the resulting outbursting behavior of the PPD. We conducted global numerical hydrodynamic simulations of PPD formation and evolution in the thin-disk limit. The consequences of metallicity were considered via its effects on the gas and dust opacity of the disk, the thickness of the magnetically active surface layer, and the temperature of the prestellar cloud core. We show that the metal-poor disks accumulate much more mass in the innermost regions as compared to the solar-metallicity counterparts. The duration of the outbursting phase also varies with metallicity; the low-metallicity disks showed more powerful luminosity eruptions with a shorter burst phase, which was confined mostly to the early, embedded stages of the disk evolution. The lowest-metallicity disks with the higher cloud core temperature showed the most significant differences. The occurrence of outbursts was relatively rare in the disks around low-mass stars, and this was especially true at the lowest metallicities. We conclude that the metal content of the disk environment can have profound effects on both the disk structure and evolution in terms of episodic accretion.