One of the public fundamental disciplines that is typically put up among the professional teaching units in universities is dance. In order for this sports project with fitness, mental health, and aesthetic functions to be widely developed in universities, the use of reasonable, scientific, and targeted teaching methods can effectively improve the instructional effect. At the same time, it has further promoted the quality of education in universities and implemented the guiding ideology of “health first.” In order to avoid the classifier’s performance-degrading effects brought on by the high dimension, this research suggests combining the classifier’s psychological stress identification algorithm with a particle swarm optimization (PSO) approach. The experimental findings reveal that the PSO-SVM algorithm, PSO-BP algorithm, improved PSO-SVM algorithm, and improved PSO-BP algorithm, respectively, have recognition rates for psychological stress of 82.50%, 84.50%, 90.17%, and 94.83%. Additionally, the recognition rates of the improved PSO classifier are significantly higher than those of the basic PSO algorithm, demonstrating the improved PSO algorithm’s strong generalization ability in optimization.