With the development of Internet technology, the speed of information dissemination and accelerated updates result in frequent discussion of topics and expressions of public opinion. In general, multi-dimensional discussion topics related to the same event are often generated in the network, and the phenomenon of multi-dimensional public opinion polarization is formed under the mutual influence of groups. This paper targets the phenomenon of multi-dimensional public opinion polarization under topic-derived situations as the research object. Firstly, this paper identifies the factors influencing multi-dimensional public opinion polarization, including the mutual influence of different topic dimensions and the interaction of viewpoints within the same topic. Secondly, the topic correlation coefficient is introduced to describe the correlation among topics in different dimensions, and the individual topic support degree is used to measure the influence of topics in different dimensions and that of information from external intervention on individual attitudes. Thirdly, a multi-dimensional public opinion polarization model is constructed by further integrating multi-dimensional attitude interaction rules. Finally, the influence of individual participation, topic status, topic correlation coefficient and external intervention information on the multi-dimensional public opinion polarization process is analyzed through simulation experiments. The simulation results show that: (1) when there is a negative correlation between multi-dimensional topics, as the number of participants on different dimensional topics becomes more consistent, the conflict between multi-dimensional topics will weaken the polarization effect of overall public opinion. However, the effect of public opinion polarization will be enhanced alongwith the enhancement in the confidence of individual opinions. (2) The intervention of external intervention information in different dimensions at different times will further form a multi-dimensional and multi-stage public opinion polarization, and when the multi-dimensional topics are negatively correlated, the intervention of external intervention information will have a stronger impact on the multi-dimensional and multi-stage public opinion polarization process. Finally, the rationality and validity of the proposed model are verified by a real case.