Studies of sentence comprehension deficits in Parkinson’s disease (PD) patients suggest that language processing involves circuits connecting subcortical and cortical regions. Anatomically segregated neural circuits appear to support different cognitive and motor functions. To investigate which functions are implicated in PD comprehension deficits, we tested comprehension, verbal working memory span, and cognitive set-switching in a non-linguistic task in 41 PD patients; we also obtained speech measurements reflecting motor sequencing processes that may be involved in articulatory rehearsal within working memory. Comprehension of sentences with center-embedded or final relative clauses was impaired when they could not be understood from lexical semantic content alone. Overall comprehension error rates correlated strongly with impaired set-switching and significantly with reduced working memory span and speech motor sequencing deficits. Correlations with comprehension of different sentence structures indicate that these impairments do not represent a single deficit; rather, PD comprehension deficits appear to arise from several independent mechanisms. Deficits in cognitive set-switching or underlying inhibitory processes may compromise the ability to process relative clauses. Deficits in verbal working memory appear to impair comprehension of long-distance dependencies. Speech sequencing correlated with neither set-switching nor verbal working memory span, consistent with their being supported by independent, segregated cortico-subcortical circuits.