We present 0.95-1.80 μm spectroscopy of the ∼12-27 M Jup companion orbiting the faint (R ∼ 13.6), young (∼120 Myr) M-dwarf 2MASS J01225093-2439505 ("2M0122-2439 B") at 1″ . 5 separation (50 AU). Our coronagraphic long-slit spectroscopy was obtained with the new high contrast imaging platform Very Large Telescope Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) during Science Verification. The unique long-slit capability of SPHERE enables spectral resolution an order of magnitude higher than other extreme AO exoplanet imaging instruments. With a low mass, cool temperature, and very red colors, 2M0122-2439 B occupies a particularly important region of the substellar color-magnitude diagram by bridging the warm directly imaged hot planets with late-M/early-L spectral types (e.g., β Pic b and ROXs 42Bb) and the cooler, dusty objects near the L/T transition (HR 8799bcde and 2MASS 1207b). We fit BT-Settl atmospheric models to our R ≈ 350 spectrum and find T eff = 1600 ± 100 K and g log( ) = 4.5 ± 0.5 dex. Visual analysis of our 2M0122-2439 B spectrum suggests a spectral type L3-L4, and we resolve shallow J-band alkali lines, confirming its low gravity and youth. Specifically, we use the Allers & Liu spectral indices to quantitatively measure the strength of the FeH, VO, KI, spectral features, as well as the overall H-band shape. Using these indices, along with the visual spectral type analysis, we classify 2M0122-2439 B as an intermediate gravity object with spectral type L3.7 ± 1.0.