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She stamped her feet to knock the mud off her shoes.
Literal
She [topic-は] foot-stamp [object-を] doing shoes [genitive-の] mud [object-を] dropped.
足踏みをする ('stomp, stamp the feet, mark time') is a noun-をする collocation: 足踏み ('foot-stamping') as the activity. 落とす in the [object]を落とす frame for 'drop / get rid of / remove' covers both literal dropping and removal: ほこりを落とす ('dust off'), 泥を落とす ('knock the mud off'), 化粧を落とす ('take off makeup'). The mud is the object being shed, not a destination.