If you use the pixel inspector (search in help, but its in the raster category in customize, commands), you can see that those dark pixels along the edge are not quite black (0, 0, 0). Without knowing how the image got like this, its very difficult to comment further.
But I just clipped your image again, using a polygon graphic and data -> export. When I do it to jpeg, there are still some errant dark pixels outside of the area of the graphic. If I export to tiff however, it all looks good.
I am using v10.2.
Perhaps you should try some different image formats (tif, img, fgdb) and see which works best.
Cheers and good luck,
Neil