When various urban functions are integrated into one location, they form a mixture of functions. The emerging big data promote an alternative way to identify mixed functions. However, current methods are largely unable to extract deep features in these data, resulting in low accuracy. In this study, we focused on recognizing mixed urban functions from the perspective of human activities, which are essential indicators of functional areas in a city. We proposed a framework to comprehensively extract deep features of human activities in big data, including activity dynamics, mobility interactions, and activity semantics, through representation learning methods. Then, integrating these features, we employed fuzzy clustering to identify the mixture of urban functions. We conducted a case study using taxi flow and social media data in Beijing, China, in which five urban functions and their correlations with land use were recognized. The mixture degree of urban functions in each location was revealed, which had a negative correlation with taxi trip distance. The results confirmed the advantages of our method in understanding mixed urban functions by employing various representation learning methods to comprehensively depict human activities. This study has important implications for urban planners in understanding urban systems and developing better strategies.