Background and Objectives: Postoperative neurological complications (NCs) are an important cause of mortality in patients with acute type A aortic dissection (ATAAD). The aim of the study was to determine the association between intraoperative risk factors and newly developed postoperative NCs in patients after emergency surgery for ATAAD. Materials and Methods: A total of 203 patients requiring emergency surgery were included in the study. Patients with preoperative neurological dysfunction, deceased on the operating table or within the first 48 h after intensive care admission, with uncertain postoperative neurologic status or with incomplete records were excluded. Results: Mean age was 57.61 ± 12.27 years. Hyperlipidemia was the most frequent comorbidity (69%). A bicuspid aortic valve was present in 12.8% of cases, severe acute aortic regurgitation was present in 29.1% of patients, and cardiac tamponade was present in 27.1% of cases. The innominate artery was the most frequently dissected supra-aortic artery in 27.1% of cases. In 65% of cases, the primary entry tear was at the level of the ascending aorta. The incidence of newly developed postoperative NCs was 39.4%. The most common surgical technique performed was supra-coronary ascending aorta and hemiarch replacement, in 53.2% of patients. Using logistic regression, cardiopulmonary bypass time (OR = 1.01; 95% CI = 1.01–1.02; p < 0.001), aortic cross-clamp time over 3 h (OR = 2.71, 95% CI = 1.43–5.14, p = 0.002) and cerebral perfusion time (OR = 1.02; 95% CI = 1.002–1.03; p = 0.027) were independently associated with newly developed postoperative NCs. Conclusions: Based on the results of the study, all efforts should be made to reduce operative times. Using a simple surgical technique, like the supra-coronary ascending aorta and hemiarch technique, whenever possible, and using a simpler technique for cerebral perfusion like unilateral cerebral perfusion via the right axillary artery, could reduce operating times.