Motivated by the fact that argumentation is intrinsically a dynamic process, the study of representational and computational aspects of dynamics in argumentation is starting to gain more traction. This is also witnessed by the most recent 2019 edition of the International Competition on Computational Models of Argumentation (ICCMA 2019), which introduced a new track focusing on dynamic argumentation frameworks. In this paper, we present an efficient Boolean satisfiability (SAT) based approach to reasoning over dynamic argumentation frameworks. In particular, based on employing incremental SAT solving, we detail algorithms covering all of the reasoning tasks—credulous and skeptical acceptance, as well as the computation of a single and all extensions—and semantics—complete, preferred, stable, and grounded—constituting the ICCMA 2019 dynamic track. Furthermore, we demonstrate empirically that an implementation of the approach is highly competitive.