We present new near-infrared Gemini Planet Imager (GPI) spectroscopy of HD 206893 B, a substellar companion orbiting within the debris disk of its F5V star. The $J$, $H$, $K1$, and $K2$ spectra from GPI demonstrate the extraordinarily red colors of the object, confirming it as the reddest substellar object observed to date. The significant flux increase throughout the infrared presents a challenging atmosphere to model with existing grids. Best-fit values vary from 1200 K to 1800 K for effective temperature and from 3.0 to 5.0 for log($g$), depending on which individual wavelength band is fit and which model suite is applied. The extreme redness of the companion can be partially reconciled by invoking a high-altitude layer of sub-micron dust particles, similar to dereddening approaches applied to the peculiar red field L-dwarf population. However, reconciling the HD 206893 B spectra with even those of the reddest low-gravity L-dwarf spectra still requires the contribution of additional atmospheric dust, potentially due to the debris disk environment in which the companion resides. Orbit fitting from four years of astrometric monitoring is consistent with a $sim$30-year period, orbital inclination of 147$^{circ}$, and semimajor axis of 10 au, well within the estimated disk inner radius of $sim$50 au. As one of very few substellar companions imaged interior to a circumstellar disk, the properties of this system offer important dynamical constraints on companion-disk interaction and provide a benchmark for substellar and planetary atmospheric study.
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