Psychopathy is associated with severe deviations in social behavior and cognition. While previous research described such cognitive and neural alterations in the processing of rather specific social information from human expressions, some open questions remain concerning central and differential neurocognitive deficits underlying psychopathic behavior. Here we investigated three rather unexplored factors to explain these deficits, first, by assessing psychopathy subtypes in social cognition, second, by investigating the discrimination of social communication sounds (speech, non-speech) from other non-social sounds, and third, by determining the neural overlap in social cognition impairments with autistic traits, given potential common deficits in the processing of communicative voice signals. The study was exploratory with a focus on how psychopathic and autistic traits differentially influence the function of social cognitive and affective brain networks in response to social voice stimuli. We used a parametric data analysis approach from a sample of 113 participants (47 male, 66 female) with ages ranging between 18 and 40 years (mean 25.59, SD 4.79). Our data revealed four important findings. First, we found a phenotypical overlap between secondary but not primary psychopathy with autistic traits. Second, primary psychopathy showed various neural deficits in neural voice processing nodes (speech, non-speech voices) and in brain systems for social cognition (mirroring, mentalizing, empathy, emotional contagion). Primary psychopathy also showed deficits in the basal ganglia (BG) system that seems specific to the social decoding of communicative voice signals. Third, neural deviations in secondary psychopathy were restricted to social mirroring and mentalizing impairments, but with additional and so far undescribed deficits at the level of auditory sensory processing, potentially concerning deficits in ventral auditory stream mechanisms (auditory object identification). Fourth, high autistic traits also revealed neural deviations in sensory cortices, but rather in the dorsal auditory processing streams (communicative context encoding). Taken together, social cognition of voice signals shows considerable deviations in psychopathy, with differential and newly described deficits in the BG system in primary psychopathy and at the neural level of sensory processing in secondary psychopathy. These deficits seem especially triggered during the social cognition from vocal communication signals.