Liquefied natural gas (LNG), recognized as the primary form for natural gas transportation, can release substantial cold energy during gasification. To make efficient use of this cold energy, this paper proposes a data-driven stochastic robust (DDSR) energy management method for the multi-stage cascade utilization of LNG cold energy in a multi-energy microgrid (MEMG) of an LNG receiving terminal. Firstly, a general scheduling model considering the flexible coupling between adjacent stages, energy losses, and electric power consumption for the cascade utilization of LNG cold energy is introduced. This model is applied to carbon capture, cryogenic power generation, and direct cooling, which are sequentially associated with the deep, medium, and shallow cooling zones of LNG cold energy, respectively. Moreover, a two-stage energy management framework is proposed to coordinate the cascade utilization of LNG cold energy with other energy resources in the MEMG. To tackle the uncertainties of renewable energy generation and various loads, a DDSR-based solution method is developed, aiming to achieve both economic benefits and solution robustness by identifying the worst-case scenarios and the corresponding worst-case probability. Accordingly, a Benders decomposition-based solution algorithm is proposed to divide the original problem into a master problem and a slave problem, which are solved iteratively. The simulation results verify the effectiveness and high efficiency of the proposed DDSR energy management method for multi-stage cascade utilization of LNG cold energy.