Developing a robust speech emotion recognition (SER) system in noisy conditions faces challenges posed by different noise properties. Most previous studies have not considered the impact of human speech noise, thus limiting the application scope of SER. In this paper, we propose a novel two-stage framework for the problem by cascading target speaker extraction (TSE) method and SER. We first train a TSE model to extract the speech of target speaker from a mixture. Then, in the second stage, we utilize the extracted speech for SER training. Additionally, we explore a joint training of TSE and SER models in the second stage. Our developed system achieves a 14.33% improvement in unweighted accuracy (UA) compared to a baseline without using TSE method, demonstrating the effectiveness of our framework in mitigating the impact of human speech noise. Moreover, we conduct experiments considering speaker gender, showing that our framework performs particularly well in different-gender mixture.