To pay with one's own money; to cover a cost personally, often implying reluctance or financial burden.
飲み会の会費は今回、私が自腹を切った。
I paid the bill for the drinking party out of my own pocket this time.
部長が急な出費を自腹を切って処理した。
The manager handled the sudden expense by paying personally.
そのプロジェクトは予算が通らず、担当者が自腹を切って試作した。
The project's budget wasn't approved, so the person in charge paid for the prototype themselves.