The increasing depletion of high-grade nickel sulfide deposits and the growing demand for nickel have intensified global interest in oxidized nickel ores (ONOs), particularly those located in Kazakhstan. This study presents a comprehensive review of the mineralogical and chemical characteristics of ONOs from the Shevchenkovskoye cobalt–nickel ore deposit and other Kazakhstan deposits, highlighting the challenges they pose for conventional beneficiation and metallurgical processing. Current industrial practices are analyzed, including pyrometallurgical, hydrometallurgical, and pyro-hydrometallurgical methods, with an emphasis on their efficiency, environmental impact, and economic feasibility. Special attention is given to the potential of hydro-catalytic leaching as a flexible, energy-efficient alternative for treating low-grade ONOs under atmospheric conditions. The results underscore the necessity of developing cost-effective and sustainable technologies tailored to the unique composition of Kazakhstani ONOs, particularly those rich in iron and magnesium. This work provides a strategic framework for future research and the industrial application of advanced leaching techniques to unlock the full potential of Kazakhstan’s nickel resources.