The ongoing deployment of residential smart meters in numerous jurisdictions has led to an influx of electricity consumption data. This information presents a valuable opportunity to suppliers for better understanding their customer base and designing more effective tariff structures. In the past, various clustering methods have been proposed for meaningful customer partitioning. This paper presents a novel finite mixture modeling framework based on C-vine copulas (CVMM) for carrying out consumer categorization. The superiority of the proposed framework lies in the great flexibility of pair copulas toward identifying multidimensional dependency structures present in load profiling data. CVMM is compared to other classical methods by using real demand measurements recorded across 2613 households in a London smart-metering trial. The superior performance of the proposed approach is demonstrated by analyzing four validity indicators. In addition, a decision tree classification module for partitioning new consumers is developed and the improved predictive performance of CVMM compared to existing methods is highlighted. Further case studies are carried out based on different loading conditions and different sets of large numbers of households to demonstrate the advantages and to test the scalability of the proposed method.