Beard but no mustache.
Stephen Scott gives possible reasons in Why Do They Dress That Way?
1) ‘Evil-looking’ European soldiers used to wear curly mustaches. Amish shaved theirs to set themselves apart.
As far as facial hair goes, married Amishmen wear beards to varying length. In some communities, unmarried men of a certain age can too.
Beards range from long and straggly-looking to short and chiseled-neat. This may reflect how progressive or conservative a group is.
Some Amish have very impressive beards. That said, a tip for travelers to Amish America: look, admire, never tug.