We experimentally investigate the evaporation of water-ethanol binary sessile droplets loaded with alumina nanoparticles on a critically inclined heated surface and compare it to the no-loading condition. In contrast to a droplet of pure fluids, several distinct and interesting phenomena observed in a binary-nanofluid droplet on a critically inclined substrate are reported for the first time. The critical angle at which a droplet begins to slide increases for ethanol-rich binary droplets up to 0.6 wt % nanoparticle loading. The critical angle for binary droplets also increases as the substrate temperature increases and as the ethanol concentration decreases for modest loading conditions. It is observed that the advancing side of a binary droplet is pinned in both the loading and no-loading scenarios, whereas the receding side is pinned in the loading case but shrinks continuously in the no-loading case. The pinning effect caused by nanoparticles results in a larger perimeter and surface area for the nanoparticle-laden droplets, enhancing the evaporation rates and significantly decreasing the lifetime of the nanoparticle-containing droplets compared to the no-loading case. Increasing the ethanol percentage in the binary droplet placed on an inclined substrate produces complex thermosolutal Marangoni convection, which becomes more affluent in the case of nanoparticles loading than the no-loading condition. The radial symmetry of the circular coffee ring structure observed on a horizontal surface is shattered in the inclined case because the droplet elongates and preferentially deposits toward the advancing side of the triple line due to the action of the body force. Despite its fundamental nature, the present study can contribute to understanding many practical applications.