Interest in edible oil extraction processes is growing interest because the final nutritional quality of the extracted oil depends on the procedure used to obtain ir. In this context, a domestic cold oil press machine is a valuable tool that avoids the use of chemicals during oil extraction, in an environmentally friendly way. Although babassu (Attalea speciosa) oil is economically important in several Brazilian regions due to its nutritional and healthy features, few studies have been conducted on the chemical composition and stability of babassu oils extracted by cold pressing. Babassu oil’s major constituents are saturated fatty acids (~86.42%), with the most prevalent fatty acids being lauric (~47.40%), myristic (15.64%), and oleic (~11.28%) acids, respectively, within the recommended range by Codex Alimentarius, presenting atherogenicity and thrombogenicity indexes favorable for human consumption. Peroxide value, Rancimat, and TGA/DSC results indicated that babassu oil is stable to oxidation. Also, macro- (Na, K, Ca, Mg, P) and micro-elements (Fe, Mn, Cr, Se, Al, and Zn) of babassu oil were determined, revealing levels below the tolerable upper intake level (ULs) for adults. These findings demonstrated that cold-press extraction using a domestic machine yielded a high-quality oil that kept oil chemical composition stable to oxidation with natural antioxidants.