The symbiotic X-ray binary Sct X-1 was suggested to be the first known neutron star accreting from a red supergiant companion. Although known for nearly 50yr, detailed characterization of the donor remains lacking, particularly due to the extremely high reddening toward the source (A_V_>~25mag). Here, we present (i) improved localization of the counterpart using Gaia and Chandra observations, (ii) the first broadband infrared spectrum (~1-5{mu}m; R~2000) obtained with SpeX on the NASA Infrared Telescope Facility, and (iii) the J-band light curve from the Palomar Gattini-IR survey. The infrared spectrum is characterized by (i) deep water absorption features (H_2_O index ~40%), (ii) strong TiO, VO, and CO features, and (iii) weak/absent CN lines. We show that these features are inconsistent with known red supergiants but suggest an M8-9 III-type O-rich Mira donor star. We report the discovery of large-amplitude ({Delta}J~3.5mag) periodic photometric variability, suggesting a pulsation period of 621+/-36 (systematic) +/-8 (statistical) days, which we use to constrain the donor to be a relatively luminous Mira (M_K_=-8.6+/-0.3mag) at a distance of 3.6_-0.7_^+0.8^kpc. Comparing these characteristics to recent models, we find the donor to be consistent with a ~3-5M_{sun}_ star at an age of ~0.1-0.3Gyr. Together, we show that Sct X-1 was previously misclassified as an evolved high-mass X-ray binary; instead, it is an intermediate-mass system with the first confirmed Mira donor in an X-ray binary. We discuss the implications of Mira donors in symbiotic X-ray binaries and highlight the potential of wide-field infrared time-domain surveys and broadband infrared spectroscopy to unveil their demographics.