Mom cleaned the mud off his shoes.

Literal

Mom [topic-は] his shoes [from-から] mud [obj-を] removed.

母さん is the casual/childlike 'mom' (contrast with the more formal 母). 落とす literally 'drop,' but here extended to 'remove/get off' — a broad verb for 'make something come off.' から marks the source (where the mud was), を the thing removed. The pattern 'take X off Y' maps onto から + を in Japanese.