Dissipative singular Dirac operators are studied in the space LA2([a,b);C2)(−∞<a<b⩽∞), that the extensions of a minimal symmetric operator in Weyl's limit-point case. We construct a selfadjoint dilation and its incoming and outgoing spectral representations, which makes it possible to determine the scattering matrix of dilation. We construct a functional model of the dissipative operator and specify its characteristic function in terms of the Titchmarsh–Weyl function of selfadjoint operator. We prove theorems on completeness of the system of eigenvectors and associated vectors of the dissipative Dirac operators.