Depending on context, dropped like a sack of potatoes to me either means to disassociate as quickly as possible or cold cock someone.
For example, if I were to explain how one of my early girlfriends broke up with me I could use the phrase, "She dropped me like a sack of potatoes." Or, if I were to explain how a boxer might have finished a fight I might say, "He dropped him like a sack of potatoes."