We examined the relationship between metaphor comprehension and verbal analogical reasoning in young adults who were either typically developing (TD) or diagnosed with Autism Spectrum Disorder (ASD). The ASD sample was highly educated and high in verbal ability, and closely matched to a subset of TD participants on age, gender, educational background, and verbal ability. Additional TD participants with a broader range of abilities were also tested. Each participant solved sets of verbal analogies and metaphors in verification formats, allowing measurement of both accuracy and reaction times. Measures of individual differences in vocabulary, verbal working memory, and autistic traits were also obtained. Accuracy for both the verbal analogy and the metaphor task was very similar across the ASD and matched TD groups. However, reaction times on both tasks were longer for the ASD group. Additionally, stronger correlations between verbal analogical reasoning and working memory capacity in the ASD group indicated that processing verbal analogies was more effortful for them. In the case of both groups, accuracy on the metaphor and analogy tasks was correlated. A mediation analysis revealed that after controlling for working memory capacity, the inter-task correlation could be accounted for by the mediating variable of vocabulary knowledge, suggesting that the primary common mechanisms linking the two tasks involve language skills.