Objectives: The effects of brain tumors located in the supplementary motor area (SMA) have so far been described mainly in the context of motor and speech disorders. There are few studies that have considered other cognitive domains, so this study aimed to fill this gap by focusing on examining attention and working memory in a population of patients with gliomas in the SMA region. Methods: This study included 50 patients diagnosed with gliomas located in the SMA who have not yet had any treatment and 57 demographically matched healthy individuals. A set of neuropsychological tests was conducted to assess attention and working memory: Digit Span from WAIS-R, Visual Elevator from TEA, Verbal Fluency Test (switching condition), and Color Trails Test (CTT). Results: The analyses showed that patients scored lower in most of the evaluated tests and indicators, namely in Digit Span-forward (t = −2.05; p = 0.022), Digit Span-backward (t = −2.63; p = 0.005), CTT-2 (t = 4.24; p = 0.001), CTT-interference (t = 2.31; p = 0.012), Visual Elevator-time (t = 1.83; p = 0.035), Visual Elevator-accuracy (t = −2.42, p = 0.010), and Verbal Fluency-switching (t = −3.41; p = 0.001). A significant relationship was also demonstrated between the grade of tumor malignancy and the results achieved in some of the neuropsychological tests. The lateralization of the tumor, the size of the lesion, and the presence of epilepsy did not prove to be particularly significant. Conclusions: Due to the significant decline in cognitive performance in terms of attention and working memory, we believe that every patient with a tumor in the SMA should undergo a detailed neuropsychological examination, which will profile their functioning and help tailor the best possible psychological care.