expression, godan verb (-su)
drink too much alcohol; overdrink
A set phrase meaning to drink excessively, often to the point of intoxication or losing control. The verb 過ごす here carries the sense of 'overdoing' or 'exceeding a limit'.
昨夜は酒を過ごして、今朝は頭が痛い。
I drank too much last night and have a headache this morning.
酒を過ごさないように気をつけ
Please be careful not to drink too much.