This study investigates the relationship between Drawing Memory and other cognitive skills in children with Autism Spectrum Disorder (ASD). Despite the growing interest in using AI and machine learning techniques to analyze drawing patterns and visual-spatial skills in ASD, the specific role of Drawing Memory remains poorly understood. We employed multiple analytical approaches to quantify these relationships and determine whether Drawing Memory can be affected by other cognitive abilities. Our dataset contains practical cognitive skill assessments measuring Age, Visual Motor Precision, Facial Memory, Spatial Vision, and Orientation. Results showed weak correlations between Drawing Memory and other cognitive skills, with correlation coefficients ranging from −0.117 to 0.062. Predictive models showed poor performance, with the best-performing Random Forest model explaining only 9.89% of the variance in Drawing Memory. Hence, it is clear that Drawing Memory operates independently of the other cognitive skills examined in this work. This provided a better understanding for cognitive development in children with ASD and help in having proper interventions and developing learning strategies for these children. The independence of Drawing Memory suggests that cognitive skills in ASD may develop along distinct stages, requiring individual educational and therapeutic approaches. Furthermore, this provides a valid motivation to study relationship between all cognitive skills.