Using observations from the first two years of the MOSFIRE Deep Evolution Field (MOSDEF) survey, we study 13 AGN-driven outflows detected from a sample of 67 X-ray, IR and/or opticallyselected AGN at z ∼ 2. The AGN have bolometric luminosities of ∼ 10 44 − 10 46 erg s −1 , including both quasars and moderate-luminosity AGN. We detect blueshifted, ionized gas outflows in the Hβ, [OIII], Hα and/or [NII] emission lines of 19% of the AGN, while only 1.8% of the MOSDEF galaxies have similarly-detected outflows. The outflow velocities span ∼300 to 1000 km s −1 . Eight of the 13 outflows are spatially extended on similar scales as the host galaxies, with spatial extents of 2.5 to 11.0 kpc. Outflows are detected uniformly across the star-forming main sequence, showing little trend with the host galaxy SFR. Line ratio diagnostics indicate that the outflowing gas is photoionized by the AGN. We do not find evidence for positive AGN feedback, in either our small MOSDEF sample or a much larger SDSS sample, using the BPT diagram. Given that a galaxy with an AGN is ten times more likely to have a detected outflow, the outflowing gas is photoionzed by the AGN, and estimates of the mass and energy outflow rates indicate that stellar feedback is insufficient to drive at least some of these outflows, they are very likely to be AGN-driven. The outflows have mass-loading factors of the order of unity, suggesting that they help regulate star formation in their host galaxies, though they may be insufficient to fully quench it.