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Here we report the detection of dust depletion in a misaligned inner disk around UX Tau A using JWST MIRI spectra. Mid-infrared (MIR) continuum "seesaw" variability was detected in this disk by Spitzer and attributed to variable shadows cast on the outer disk by the inner disk. The JWST MIRI spectrum of UX Tau A also shows seesaw variability, but with a significant decrease of emission shortwards of 10 micron to nearly photospheric levels. We argue that UX Tau A's MIR continuum variability is due to depletion of dust in a misaligned inner disk. We speculate that this dust depletion occurs because the inner disk is misaligned from the outer disk, which can disrupt the replenishment of the inner disk from the outer disk. Using contemporaneous measurements of the mass accretion rate of UX Tau A and estimating the amount of dust necessary to produce the MIR excess in the Spitzer observations, we estimate a minimum dust depletion timescale of ~0.1 yr. These observations show that we can indirectly detect the signatures of misaligned inner disks through MIR continuum variability and that in some cases the inner disk may be significantly depleted of dust and become optically thin.