We present mid-infrared spectral mapping observations of the core-collapse supernova remnant 1E 0102.2-7219 in the Small Magellanic Cloud using the InfraRed Spectrograph (IRS) on the Spitzer Space Telescope. The remnant shows emission from fine structure transitions of neon and oxygen as well as continuum emission from dust. Comparison of the mid-IR dust emission with observations at x-ray, radio and optical wavelengths shows that the dust is associated with the supernova ejecta and is thus newly formed in the remnant. The spectrum of the newly formed dust is well reproduced by a model that includes 3x10^-3 solar masses of amorphous carbon dust at 70 K and 2x10^-5 solar masses of Mg2SiO4 (forsterite) at 145 K. Our observations place a lower limit on the amount of dust in the remnant since we are not sensitive to the cold dust in the unshocked ejecta. We compare our results to observations of other core-collapse supernovae and remnants, particularly Cas A where very similar spectral mapping observations have been carried out. We observe a a factor of ~10 less dust in E 0102 than seen in Cas A, although the amounts of amorphous carbon and forsterite are comparable.