Learner's definition of MUD
: soft, wet dirt
He tracked mud into the house.
His shoes were covered with mud. = His shoes were caked in/with mud.
The car was stuck in the mud.
as clear as mudinformal
: very difficult to understand : not clear at all
drag someone's name through the mud
sling/throw mudchiefly US
: to publicly say false or bad things about someone (such as a political opponent) in order to harm that person's reputation
your name is mudinformal
◊ If your name is mud people do not like or trust you.