The clinical profiles of individuals with post-stroke aphasia demonstrate considerable variation in the presentation of symptoms. Recent aphasiological studies have attempted to account for this individual variability using a multivariate data-driven approach (principal component analysis) on an extensive neuropsychological and aphasiological battery, to identify fundamental domains of post-stroke aphasia. These domains mainly reflect phonology, semantics and fluency; however, these studies did not account for variability in response to different forms of connected speech, i.e. discourse genres. In the current study, we initially examined differences in the quantity, diversity and informativeness between three different discourse genres, including a simple descriptive genre and two naturalistic forms of connected speech (storytelling narrative, and procedural discourse). Subsequently, we provided the first quantitative investigation on the multidimensionality of connected speech production at both behavioural and neural levels. Connected speech samples across descriptive, narrative, and procedural discourse genres were collected from 46 patients with chronic post-stroke aphasia and 20 neurotypical adults. Content analyses conducted on all connected speech samples indicated that performance differed across discourse genres and between groups. Specifically, storytelling narratives provided higher quantities of content words and lexical diversity compared to composite picture description and procedural discourse. The analyses further revealed that, relative to neurotypical adults, patients with aphasia, both fluent and non-fluent, showed reduction in the quantity of verbal production, lexical diversity, and informativeness across all discourses. Given the differences across the discourses, we submitted the connected speech metrics to principal component analysis alongside an extensive neuropsychological/aphasiological battery that assesses a wide range of language and cognitive skills. In contrast to previous research, three unique orthogonal connected speech components were extracted in a unified model, reflecting verbal quantity, verbal quality, and motor speech, alongside four core language and cognitive components: phonological production, semantic processing, phonological recognition, and executive functions. Voxel-wise lesion-symptom mapping using these components provided evidence on the involvement of widespread cortical regions and their white matter connections. Specifically, left frontal regions and their underlying white matter tracts corresponding to the frontal aslant tract and the anterior segment of the arcuate fasciculus were particularly engaged with the quantity and quality of fluent connected speech production while controlling for other co-factors. The neural correlates associated with the other language domains align with existing models on the ventral and dorsal pathways for language processing.