Sequential regression was used to evaluate whether language-related working memory components uniquely predict reading and writing achievement beyond cognitive-linguistic translation for students in Grades 4 through 9 (N = 103) with specific learning disabilities (SLDs) in subword handwriting (dysgraphia, n = 25), word reading and spelling (dyslexia, n = 60), or oral and written language (oral and written language learning disabilities, n = 18). That is, SLDs are defined on the basis of cascading level of language impairment (subword, word, and syntax/text). A five-block regression model sequentially predicted literacy achievement from cognitive-linguistic translation (Block 1); working memory components for word-form coding (Block 2), phonological and orthographic loops (Block 3), and supervisory focused or switching attention (Block 4); and SLD groups (Block 5). Results showed that cognitive-linguistic translation explained an average of 27% and 15% of the variance in reading and writing achievement, respectively, but working memory components explained an additional 39% and 27% of variance. Orthographic word-form coding uniquely predicted nearly every measure, whereas attention switching uniquely predicted only reading. Finally, differences in reading and writing persisted between dyslexia and dysgraphia, with dysgraphia higher, even after controlling for Block 1 to 4 predictors. Differences in literacy achievement between students with dyslexia and oral and written language learning disabilities were largely explained by the Block 1 predictors. Applications to identifying and teaching students with these SLDs are discussed.