Background: Aortic valve stenosis (AVS) is a common valvular heart disease affecting millions of people worldwide. It leads to significant neurocognitive and neuropsychological impairments, impacting patients’ quality of life. Objective: The objective of this article is to identify and discuss the potential neurocognitive effects on patients with aortic stenosis before and after undergoing surgical aortic valve replacement (SAVR). Method: Our study involved the assessment of 64 patients undergoing aortic valve replacement (SAVR) using a neurocognitive evaluation comprising a battery of 11 different cognitive tests. These tests were designed to analyze the patients’ overall cognitive functioning, executive abilities, short- and long-term memory, and attentional performance. The tests were administered to patients before the aortic valve surgery (T0) and after the surgery (T1). From a statistical perspective, numerical variables are presented as means (±standard deviation) and medians (IQR), while categorical variables are presented as counts and percentages. Normality was assessed using the Shapiro–Wilk test. T0 and T1 scores were compared with the Wilcoxon signed rank test, with p < 0.05 considered significant. Analyses were performed using SAS version 9.4. Results: Conducted as part of a fully financed Italian Ministry of Health project (RF-2016-02361069), the study found that most patients showed normal cognitive functioning at baseline. Cognitive assessments showed that executive functions, attention, language, and semantic knowledge were within the normal range for the majority of participants. After SAVR, cognitive outcomes remained stable or improved, particularly in executive functions and language. Notably, verbal episodic memory demonstrated significant improvement, with the percentage of patients scoring within the normal range on the BSRT increasing from 73.4% at T0 to 92.2% at T1 (p < 0.0001). However, visuospatial and visuoconstructive abilities showed stability or slight decline, while attentional skills remained relatively stable. The Clock Drawing Test indicated the maintenance of cognitive functions. Conclusions: The findings of our study indicate a global stability in cognitive status among patients after undergoing SAVR, with significant improvement noted in verbal episodic memory. While other cognitive domains did not demonstrate statistically significant changes, these insights are valuable for understanding the cognitive effects of SAVR and can guide future research and clinical practice in selecting the most effective surgical and rehabilitative options for patients. Monitoring cognitive outcomes in patients undergoing aortic valve replacement surgery remains crucial.