Background: Significant changes in the accessibility and viability of health services have been observed during the COVID-19 period, particularly in vulnerable groups such as cancer patients. In this study, we described the impact of radical practice and perceived changes on cancer patients’ mental well-being and investigated potential outcome descriptors. Methods: Generalized anxiety disorder assessment (GAD-7), patient health (PHQ-9), and World Health Organization-five well-being index (WHO-5) questionnaires were used to assess anxiety, depression, and mental well-being. Information on participants, disease baseline information, and COVID-19-related questions were collected, and related explanatory variables were included for statistical analysis. Results: The mean score values for anxiety, depression, and mental well-being were 4.7 ± 5.53, 4.9 ± 6.42, and 72.2 ± 18.53, respectively. GAD-7 and PHQ-9 scores were statistically associated (p < 0.001), while high values of GAD-7 and PHQ-9 questionnaires were related to low values of WHO-5 (p < 0.001).Using the GAD-7 scale, 16.2% of participants were classified as having mild anxiety (GAD-7 score: 5–9).Mild to more severe anxiety was significantly associated with a history of mental health conditions (p = 0.01, OR = 3.74, 95% CI [1.372–10.21]), and stage category (stage III/IV vs. I/II, p = 0.01, OR = 3.83, 95% CI [1.38–10.64]. From the participants, 36.2% were considered to have depression (PHQ-9 score ≥ 5). Depression was related with older patients (p = 0.05, OR = 1.63, 95% CI [1.16–2.3]), those with previous mental health conditions (p = 0.03, OR = 14.24, 95% CI [2.47–81.84]), those concerned about the COVID-19 impact on their cancer treatment (p = 0.027, OR = 0.19, 95% CI [0.045–0.82]) or those who felt that COVID-19 pandemic has affected mental health (p = 0.013, OR = 3.56, 95% CI [1.30–9.72]). Additionally, most participants (86.7%) had a good well-being score (WHO-5score ≥ 50). Mental well-being seemed more reduced among stage I–III patients than stage IV patients (p = 0.014, OR = 0.12, 95% CI [0.023–0.65]). Conclusion: There is a necessity for comprehensive cancer care improvement. These patients’ main concern related to cancer therapy, yet the group of patients who were mentally affected by the pandemic should be identified and supported.