Background: The negative effect of COVID-19 pandemic on college students’ mental health is well-demonstrated. The aim of this study is to assess the impact of the pandemic on the students of Aristotle University of Thessaloniki (Northern Greece), in terms of stress, anxiety, and depression, and to analyze the probable correlation of various social and phycological factors. Methods: The survey was conducted in the form of a questionnaire, which was first distributed in November 2020 and then re-launched in November 2021. The evaluation was carried out through the DASS21 screening tool. Associations regarding participants’ characteristics and the three variables (stress, anxiety, and depression) were investigated with Pearson’s chi-squared (Χ2) test. Results: The first-year results (November 2020) revealed severe prevalence of stress, anxiety, and depression (37.4%, 27.2% and 47% respectively). The second-year results (November 2021) revealed a significant augmentation in all three variables, mainly for the extreme severe scales (47.3%, 41.1% and 55% respectively). Participants who were receiving psychiatric treatment exhibited higher levels of stress, anxiety, and depression, especially during the second year of the pandemic (p-Value < 0.00001). Female students’ mental health was at higher risk, as elevated prevalence of negative symptoms was observed (p-Value < 0.00001). Conclusions: The community of Aristotle University of Thessaloniki has been greatly affected during the last 2 years. The inherent risks of the confinement measures on students’ well-being and mental health are undeniable. Recurrent annual psychological evaluation in universities and colleges is strongly advised.