She stirred her coffee with a spoon.

Literal

She [topic-は] spoon [with-で] coffee [object-を] stirred.

Stirring with a spoon, expressed with the cleaner instrumental で marking the tool — the unmarked everyday choice. で and ~を使って both express instrumental meaning, but で is shorter and treats the tool as background; ~を使って highlights the act of using it. コーヒー is one of the older Western loanwords in Japanese, entering through Dutch koffie during the Edo period (when the Dutch were the only Westerners trading via Nagasaki). That Dutch route is why several early loanwords have origins one wouldn't guess from English.