In light of the growing impact of disinformation on social, economic, and political landscapes, accurate and efficient identification methods are increasingly critical. This paper introduces HyperGraphDis, a novel approach for detecting disinformation on Twitter that employs a hypergraph-based representation to capture (i) the intricate social structures arising from retweet cascades, (ii) relational features among users, and (iii) semantic and topical nuances. Evaluated on four Twitter datasets -- focusing on the 2016 U.S. presidential election and the COVID-19 pandemic -- HyperGraphDis outperforms existing methods in both accuracy and computational efficiency, underscoring its effectiveness and scalability for tackling the challenges posed by disinformation dissemination. HyperGraphDis displays exceptional performance on a COVID-19-related dataset, achieving an impressive F1 score (weighted) of approximately 89.5%. This result represents a notable improvement of around 4% compared to the other state-of-the-art methods. Additionally, significant enhancements in computation time are observed for both model training and inference. In terms of model training, completion times are accelerated by a factor ranging from 2.3 to 7.6 compared to the second-best method across the four datasets. Similarly, during inference, computation times are 1.3 to 6.8 times faster than the state-of-the-art.