ABSTRACT Multibody dynamical interactions of binaries with other objects are one of the main driving mechanisms for the evolution of star clusters. It is thus important to bring our understanding of three-body interactions beyond the commonly employed point-particle approximation. To this end, we here investigate the hydrodynamics of three-body encounters between star–black hole (BH) binaries and single stars, focusing on the identification of final outcomes and their long-term evolution and observational properties, using the moving-mesh hydrodynamics code AREPO. This type of encounter produces five types of outcomes: stellar disruption, stellar collision, weak perturbation of the original binary, binary member exchange, and triple formation. The two decisive parameters are the binary phase angle, which determines which two objects meet at the first closest approach, and the impact parameter, which sets the boundary between violent and non-violent interactions. When the impact parameter is smaller than the semimajor axis of the binary, tidal disruptions and star-BH collisions frequently occur when the BH and the incoming star first meet, while the two stars mostly merge when the two stars meet first instead. In both cases, the BHs accrete from an accretion disc at super-Eddington rates, possibly generating flares luminous enough to be observed. The stellar collision products either form a binary with the BH or remain unbound to the BH. Upon collision, the merged stars are hotter and larger than the main sequence stars of the same mass at similar age. Even after recovering their thermal equilibrium state, stellar collision products, if isolated, would remain hotter and brighter than main sequence stars until becoming giants.