。
She's wearing a watch just like mine.
Literal
She [topic-は] mine [as-と] same watch [object-を] is-wearing.
私のと同じ ('the same as mine') is a tight construction worth dissecting: 私の is 'mine' (の as a nominalizer / pronoun, replacing the implied 時計), the と marks the comparison target, and 同じ ('same') closes the comparison — together, 'the same as mine.' 時計をする ('to wear a watch') uses する rather than はめる ('put on') — する is broadly used for wearing accessories like watches, ties, glasses (indirectly via かける), and rings, while 着る is for clothing on the torso and 履く for shoes/pants. Each garment category in Japanese has its own 'wear' verb.