FIG. 1 is a perspective view of a new and ornamental design for a dual-sided automotive wash mitt; FIG. 2 is a second perspective view thereof; FIG. 3 is a front elevation view thereof; FIG. 4 is a side elevation view thereof, the opposite side being a mirror image; FIG. 5 is a top plan view thereof; FIG. 6 is a bottom plan view thereof; and, FIG. 7 is an end elevation view thereof.