We present detailed studies of a z = 2.12 submillimeter galaxy, ALESS67.1, using sub-arcsecond resolution ALMA, adaptive optics-aided VLT/SINFONI, and Hubble Space Telescope (HST)/CANDELS data to investigate the kinematics and spatial distributions of dust emission (870 μm continuum), 12CO(J = 3–2), strong optical emission lines, and visible stars. Dynamical modeling of the optical emission lines suggests that ALESS67.1 is not a pure rotating disk but a merger, consistent with the apparent tidal features revealed in the HST imaging. Our sub-arcsecond resolution data set allows us to measure half-light radii for all the tracers, and we find a factor of 4–6 smaller sizes in dust continuum compared to all the other tracers, including 12CO; also, ultraviolet (UV) and Hα emission are significantly offset from the dust continuum. The spatial mismatch between the UV continuum and the cold dust and gas reservoir supports the explanation that geometrical effects are responsible for the offset of the dusty galaxy on the IRX–β diagram. Using a dynamical method we derive an {α }{CO}=1.8+/- 1.0, consistent with other submillimeter galaxies (SMGs) that also have resolved CO and dust measurements. Assuming a single {α }{CO} value we also derive resolved gas and star formation rate surface densities, and find that the core region of the galaxy (≲ 5 kpc) follows the trend of mergers on the Schmidt–Kennicutt relationship, whereas the outskirts (≳ 5 kpc) lie on the locus of normal star-forming galaxies, suggesting different star formation efficiencies within one galaxy. Our results caution against using single size or morphology for different tracers of the star formation activity and gas content of galaxies, and therefore argue the need to use spatially resolved, multi-wavelength observations to interpret the properties of SMGs, and perhaps even for z> 1 galaxies in general.