After 30 minutes, a man appeared telling us that he had taken our suitcases by mistake.

by 在这里表示"通过某种方式"或"由于某种原因"。 mistake 是名词，意思是"错误、误会"。 by mistake 是一个固定短语，表示"由于错误、无意中、不小心"，指非故意的行为。