Working memory load can modulate speech perception. However, since speech perception and working memory are both complex functions, it remains elusive how each component of the working memory system interacts with each speech processing stage. To investigate this issue, we concurrently measure how the working memory load modulates neural activity tracking three levels of linguistic units, i.e., syllables, phrases, and sentences, using a multiscale frequency-tagging approach. Participants engage in a sentence comprehension task and the working memory load is manipulated by asking them to memorize either auditory verbal sequences or visual patterns. It is found that verbal and visual working memory load modulate speech processing in similar manners: Higher working memory load attenuates neural activity tracking of phrases and sentences but enhances neural activity tracking of syllables. Since verbal and visual WM load similarly influence the neural responses to speech, such influences may derive from the domain-general component of WM system. More importantly, working memory load asymmetrically modulates lower-level auditory encoding and higher-level linguistic processing of speech, possibly reflecting reallocation of attention induced by mnemonic load.