She made the same mistake she did last time.

Literal

She [topic-は] this-time-before [with-と] same mistake [object-を] did.

~と同じ ('the same as X') is the standard frame for marking equivalence — と here is the comitative of comparison, taking the standard against which X is measured. The full pattern XとYは同じ means 'X and Y are the same.' まちがいをする is the light-verb construction for 'to make a mistake' — まちがい ('mistake, error') paired with する as a productive way to verbalize abstract nouns. Note: in casual speech you'd often hear 同じ間違いをした as a flat statement; the explicit この前と adds the specific past reference.