An Etymological Dictionary of the German Language/Annotated/Schmutz
Schmutz, masculine, ‘dirt, filth,’ from the equivalent Middle High German smuz (-tzes), masculine, allied to Middle High German smotzen, ‘to be dirty’; also to Dutch smet, ‘spot, dirt,’ smetten, ‘to get stained,’ smodderen, ‘to soil,’ English smut, verb and substantive, Middle English bismitten, bismoteren, bismudden, ‘to stain, soil.’ It is uncertain whether these words are late graded forms of Middle High German smitzen, ‘to rub over.’