The existence of a scattering map from the event horizon to the Cauchy horizon of a black hole from the Kerr-Newman(-anti)-de Sitter (KN(A)dS) family allows for the study of the stability of the Cauchy horizon, and is therefore a necessary first step in understanding the Cosmic Censorship Conjecture. Following work done on Reissner-Nordström (Penrose and Simpson, waves; Chandrasekhar and Hartle, waves; Kehle and Shlapentokh-Rothman, scalar fields; Häfner and Nicolas and Mokdad, Dirac fields), we construct the first scattering theory in the interior of KN(A)dS, of Dirac fields. More particularly, we show existence, uniqueness and asymptotic completeness of scattering data for Dirac fields from the event horizon to the Cauchy horizon. Our approach relies on dynamic scattering: the construction of wave operators for a time-dependent Hamiltonian.