With the data landscape of the universe expands every second every day by leaps and bound, the data value also increases unprecedentedly. Particularly, the disruptive use of data in location tracking, predictive policing, fraud detection, healthcare, advertising media, and entertainment has already revitalized personal data in many ways. But massive amassing of data also gives rise to new issues regarding the Big Data effects, including privacy invasion, data breaches, and cyber threats, etc. Taking effective efforts for mitigating the risks of data explosion thus becomes indispensable for companies, organizations, and societies alike. In such background, this paper attempts to focus on the ways how the data minimization approach mitigates such risks, and how this approach as a concept is being incorporated in legal instruments globally. After exploring practical methods of applying data minimization, the paper concludes by delineating the way out of the existing dilemmas so created in the face of Big Data.