She has gone off shopping.

Literal

She [topic-は] shopping [to-に] went [end-up-てしまいました].

~てしまう (here in polite past ~てしまいました) attached to 行く: 'has gone' with a sense of finality, often with mild regret or resignation — she's already left, can't be reached. Casual contraction: 行っちゃった.