This study combines affective computing and cognitive analysis to delve into the realm of emotional exploration within poetry translation. It investigates the viability and potency of employing a quantitative-qualitative approach in poetry translation critique, exploring pathways for leveraging artificial intelligence to enrich methodological improvements and innovations in literary translation criticism. Using a sentiment analysis platform with limited human intervention, this study computes and quantitatively analyses the sentiments of translations of several versions of Shakespeare’s Sonnets, which is then complemented by qualitative analysis methods such as cognitive linguistics for textual observation. The method of quantitative analysis significantly improves the efficiency of data acquisition and processing, and helps to visually present the data, while the auxiliary qualitative analysis helps to excavate the deep mechanism behind the data of sentiments. Therefore, combining both paradigms is not only practical but also enhances analytical efficacy in poetry translation criticism.