The nature of semantic knowledge – conceptual information stored in the brain – is highly debated in the field of cognitive science. Experimental and clinical data specify various cortical regions involved in the processing of meaning. Those include semantic hubs that take part in semantic processing in general as well as sensorimotor areas that process specific conceptual categories according to their modality. Biologically inspired neurocomputational models can help adjudicate between different theories about the exact roles of those regions in the functioning of the semantic system. Here, we used an existing neuroanatomically constrained model of frontotemporal brain areas implicated in language acquisition and grounding. We adapted it to replicate and explain the effects of semantic dementia on word processing abilities. Semantic dementia is a disease characterized by semantic knowledge deterioration that correlates with neural damage in the anterior temporal lobe. The behavior of our model is in accordance with clinical data – namely, word recognition performance decreases as SD lesions progress, whereas word repetition abilities remain preserved, or are less affected. Furthermore, our model makes novel predictions about category-specific effects of SD – namely, our simulation results indicate that word processing should be more impaired for object-than for action-related words, and that white matter degradation should lead to more severe consequences than the same proportion of grey matter degradation. The present results provide a mechanistic, cortical-level explanatory account of a range of language impairments as observed in clinical populations during the onset and progress of semantic dementia.