The candidates started 'slinging mud' (at each other) early in the campaign.
His shoes were covered with 'mud'. = His shoes were caked in/with 'mud'.
The scandal ruined his reputation and now 'his name is mud'.
(..) while we were out? Let me think. No! Edith! What did you put on my desk? A mud pie. You're never gonna get adopted, Edith. You know that, don't you? - Yeah, I know. - Good. So, how did it go, girls? (..)2010 Despicable Me