Learn German: Sie mischen ein Glas Sand mit der Asche. - They mix a glass of sand with the ash.

This is a partitive apposition. In German, when a noun expresses a quantity or measurement (like ein Glas), the substance being measured (Sand) is placed right next to it without any extra words. You do not use von or the genitive case for simple materials.

Since ein Glas is the direct object here, what case is Sand in?

It is also in the accusative case. In a partitive apposition, the material noun takes the same case as the measurement noun. You cannot see the accusative ending on Sand because it is a bare noun without an article, but it structurally matches the case of ein Glas.

If I added an adjective, like 'dry sand', would I need to use the genitive case then?

You have a choice. You can keep the apposition and put the adjective in the same case as the unit: ein Glas trockenen Sand (accusative). However, once an adjective is added, the partitive genitive (ein Glas trockenen Sandes) or von plus the dative case (ein Glas von trockenem Sand) also become grammatically correct and are often used in formal writing.

Why does die Asche change to der Asche in this sentence?