We use the Spectrographic Areal Unit for Research on Optical Nebulae and Gemini Multi-Object Spectrograph integral-field spectrographs to observe the active galactic nucleus (AGN) powered outflow in NGC 1266. This unusual galaxy is relatively nearby (D = 30 Mpc), allowing us to investigate the process of AGN feedback in action. We present maps of the kinematics and line strengths of the ionized gas emission lines Hα, Hβ, [O iii], [O i], [N ii] and [S ii], and report on the detection of sodium D absorption. We use these tracers to explore the structure of the source, derive the ionized and atomic gas kinematics, and investigate the gas excitation and physical conditions. NGC 1266 contains two ionized gas components along most lines of sight, tracing the ongoing outflow and a component closer to the galaxy systemic, the origin of which is unclear. This gas appears to be disturbed by a nascent AGN jet. We confirm that the outflow in NGC 1266 is truly multiphase, containing radio plasma, atomic, molecular and ionized gas and X-ray emitting plasma. The outflow has velocities of up to ±900 km s−1 away from the systemic velocity and is very likely to remove significant amount of cold gas from the galaxy. The low-ionization nuclear emission region-like line emission in NGC 1266 is extended, and it likely arises from fast shocks caused by the interaction of the radio jet with the interstellar medium. These shocks have velocities of up to 800 km s−1, which match well with the observed velocity of the outflow. Sodium D equivalent width profiles are used to set constraints on the size and orientation of the outflow. The ionized gas morphology correlates with the nascent radio jets observed in 1.4 and 5 GHz continuum emission, supporting the suggestion that an AGN jet is providing the energy required to drive the outflow.