We present Spitzer/IRS spectral mapping observations of the luminous infrared galaxy Arp 299 (IC 694 + NGC 3690) covering the central ~45'' ~ 9 kpc. The integrated mid-IR spectrum of Arp 299 is similar to that of local starbursts despite its strongly interacting nature and high-IR luminosity, L _IR ~ 6 × 10¹¹ L _☉. This is explained because the star formation (probed by, e.g., high [Ne III]15.56 μm/[Ne II]12.81 μm line ratios) is spread across at least 6-8 kpc. Moreover, a large fraction of this star formation is taking place in young regions of moderate mid-IR optical depths such as the C+C' complex in the overlap region between the two galaxies and in H II regions in the disks of the galaxies. It is only source A, the nuclear region of IC 694, which shows the typical mid-IR characteristics of ultraluminous infrared galaxies (ULIRGs; L _IR > 10¹² L _☉), that is, very compact (less than 1 kpc) and dust-enshrouded star formation resulting in a deep silicate feature and moderate equivalent widths of the polycyclic aromatic hydrocarbons. The nuclear region of NGC 3690, known as source B1, hosts a low-luminosity active galactic nucleus (AGN) and is surrounded by regions of star formation. Although the high-excitation [Ne V]14.32 μm line typical of AGN is not detected in B1, its upper limit is consistent with the value expected from the X-ray luminosity. The AGN emission is detected in the form of a strong hot-dust component that accounts for 80%-90% of the 6 μm luminosity of B1. The similarity between the Arp 299 integrated mid-IR spectrum and those of high-z ULIRGs suggests that Arp 299 may represent a local example, albeit with lower IR luminosity and possibly higher metallicity, of the star formation processes occurring at high-z.