We present a 0.5-2.2 micron scattered light spectrum of the circumstellar disk around TW Hya from a combination of spatially resolved HST STIS spectroscopy and NICMOS coronagraphic images of the disk. We investigate the morphology of the disk at distances > 40 AU over this wide range of wavelengths, and identify the presence of a depression in surface brightness at ~80 AU that could be caused by a gap in the disk. Additionally, we quantify the surface brightness, azimuthal symmetry, and spectral character of the disk as a function of radius. Our analysis shows that the scattering efficiency of the dust is largely neutral to blue over the observed wavelengths. We model the disk as a steady alpha-disk with an ad hoc gap structure. The thermal properties of the disk are self-consistently calculated using a three-dimensional radiative transfer code that uses ray-tracing to model the heating of the disk interior and scattered light images. We find a good fit to the data over a wide range of distances from the star if we use a model disk with a partially filled gap of 30% depth at 80 AU and with a self-similar truncation knee at 100 AU. The origin of the gap is unclear, but it could arise from a transition in the nature of the disk's dust composition or the presence of a planetary companion. Based on scalings to previous hydrodynamic simulations of gap opening criteria for embedded proto-planets, we estimate that a planetary companion forming the gap could have a mass between 6-28 M_Earth. ; Comment: To appear in ApJ online on June 14; 43 pages, 14 figures