。
Field mice ate up all the farmer's grain.
Literal
Field-mouse [subj-が] farmhouse [gen-の] grain [obj-を] eat-up-[go-ていった].
食べ尽くす ('eat up completely') is a compound: 食べる + 尽くす ('exhaust'). The auxiliary 尽くす adds 'exhaustively, completely' to any action verb — 使い尽くす ('use up'), 書き尽くす ('write exhaustively'). The final ~ていった marks the action as receding into the past or progressing away from the speaker's present.