We present near-infrared integral field spectroscopy data obtained with Very Large Telescope/Spectrograph for INtegral Field Observations in the Near Infrared (SINFONI) of `the Teacup galaxy'. The nuclear K-band (1.95-2.45 μm) spectrum of this radio-quiet type-2 quasar reveals a blueshifted broad component of FWHM ˜ 1600-1800 km s-1 in the hydrogen recombination lines (Pa α, Br δ and Br γ) and also in the coronal line [Si vi] λ1.963 μm. Thus, the data confirm the presence of the nuclear ionized outflow previously detected in the optical range and reveal its coronal counterpart. Both the ionized and coronal nuclear outflows are resolved, with seeing-deconvolved full widths at half-maximum of 1.1 ± 0.1 and 0.9 ± 0.1 kpc along position angle (PA) ˜ 72°-74°. This orientation is almost coincident with the radio axis (PA = 77°), suggesting that the radio jet could have triggered the nuclear outflow. In the case of the H2 lines, we do not require a broad component to reproduce the profiles, but the narrow lines are blueshifted by ˜50 km s-1 on average from the galaxy systemic velocity. This could be an indication of the presence of a nuclear molecular outflow, although the bulk of the H2 emission in the inner ˜2 arcsec (˜3 kpc) of the galaxy follows a rotation pattern. We find evidence for kinematically disrupted gas (FWHM > 250 km s-1) at up to 5.6 kpc from the AGN, which can be naturally explained by the action of the outflow. The narrow component of [Si vi] is redshifted with respect to the systemic velocity, unlike any other emission line in the K-band spectrum. This indicates that the region where the coronal lines are produced is not cospatial with the narrow-line region.