The growing body of creativity research involves Artificial Intelligence (AI) and Machine learning (ML) approaches to automatically evaluating creative solutions. However, numerous challenges persist in evaluating the creativity dimensions and the methodologies employed for automatic evaluation. This paper contributes to this research gap with a scoping review that maps the Natural Language Processing (NLP) approaches to computations of different creativity dimensions. The review has two research objectives to cover the scope of automatic creativity evaluation: to identify different computational approaches and techniques in creativity evaluation and, to analyze the automatic evaluation of different creativity dimensions. As a first result, the scoping review provides a categorization of the automatic creativity research in the reviewed papers into three NLP approaches, namely: text similarity, text classification, and text mining. This categorization and further compilation of computational techniques used in these NLP approaches help ameliorate their application scenarios, research gaps, research limitations, and alternative solutions. As a second result, the thorough analysis of the automatic evaluation of different creativity dimensions differentiated the evaluation of 25 different creativity dimensions. Attending similarities in definitions and computations, we characterized seven core creativity dimensions, namely: novelty, value, flexibility, elaboration, fluency, feasibility, and others related to playful aspects of creativity. We hope this scoping review could provide valuable insights for researchers from psychology, education, AI, and others to make evidence-based decisions when developing automated creativity evaluation.