This is the author accepted manuscript. The final version is available from the American Astronomical Society via the DOI in this record.Type Ia supernovae (SNe Ia) originate from the thermonuclear explosion of carbon-oxygen white dwarfs (CO WDs), giving rise to luminous optical transients. A relatively common variety of subluminous SNe Ia events, referred to as SNe Iax, are believed to arise from the failed detonation of a CO WD. In this paper, we explore failed detonation SNe Ia in the context of the double-degenerate channel of merging white dwarfs. In particular, we have carried out the first fully three-dimensional simulation of the merger of a ONe WD with a CO WD. While the hot, tidally-disrupted carbon-rich disk material originating from the CO WD secondary is readily susceptible to detonation in such a merger, the ONe WD primary core is not. This merger yields a failed detonation, resulting in the ejection of a small amount of mass, and leaving behind a kicked, super-Chandrasekhar ONe WD remnant enriched by the fallback of the products of nuclear burning. The resulting outburst is a rapidly-fading optical transient with a small amount of radioactive 56Ni powering the light curve. Consequently, the ONe-CO WD merger naturally produces a very faint and rapidly-fading transient, fainter even than the faintest Type Iax events observed to date, such as SN 2008ha and SN 2010ae. More massive ONe primaries than considered here may produce brighter and longer-duration transients.The work of P.L-A. and E.G.-B. was partially funded by the MINECO AYA2014-59084-P grant and by the AGAUR. RTF thanks the Institute for Theory and Computation at the Harvard-Smithsonian Center for Astrophysics for visiting support during which a portion of this work was undertaken. RTF acknowledges support from NASA 80NSSC18K1013. This work used the Extreme Science and Engineering Discovery Environment (XSEDE) Stampede 2 supercomputer at the University of Texas at Austin’s Texas Advanced Computing Center through allocation TG-AST100038, supported by National Science Foundation grant number ACI-1548562 (Towns et al. 2014).