This exploratory mixed-methods study aimed to explore how students' perceptions of positive and negative teacher-student relationships influence their classroom engagement and academic progress. The data in the quantitative phase came from 157 undergraduate, graduate, and postgraduate students at Government Brojomohun College in Bangladesh who participated in a Google-based survey questionnaire posted on Facebook groups, and a semi-structured interview of eight students was conducted via the Zoom platform. The qualitative data were interpreted and analyzed based on the themes that emerged from literature, open-ended survey questions, and interviews. To acquire a deeper comprehension of qualitative data, quantitative data were presented and analyzed statistically. The findings revealed that college students' positive perceptions of TSR greatly improve their behavioral engagement, emotional engagement, and cognitive engagement in the classroom, as well as their academic achievement, whereas their negative perceptions of TSR significantly hinder all types of classroom engagement and academic achievement. However, this study also found that some students' positive and negative relationships with teachers have no impact on their classroom engagement and academic achievement. This study makes an important contribution to the existing literature by elucidating college students' perceptions of TSR in terms of its positive and negative perceptions, as well as its impact on classroom engagement and academic achievement in college education. The implications and limitations are discussed.