We present low-resolution near-infrared spectra of discoveries from an all-sky proper motion search conducted using multi-epoch data from the Wide-field Infrared Survey Explorer. Using the data from NEOWISE, along with the AllWISE catalog, Schneider et al. (2016, J/ApJ/817/112) conducted an all-sky proper motion survey to search for nearby objects with high proper motions. Here, we present a follow-up spectroscopic survey of 65 of their discoveries, which focused primarily on potentially nearby objects (d<25 pc), candidate late-type brown dwarfs (>=L7), and subdwarf candidates. We found 31 new M dwarfs, 18 new L dwarfs, and 11 new T dwarfs. Of these, 13 are subdwarfs, including one new sdL1 and two new sdL7s. Eleven of these discoveries, with spectral types ranging from M7 to T7 (including one subdwarf) are predicted to be within 25 pc, adding to the number of known objects in the solar neighborhood. We also discovered three new early-type T subdwarf candidates, one sdT1, one sdT2, and one sdT3, which would increase the number of known early-type T subdwarfs from two to five.