Listening to speech with poor signal quality is challenging. Neural speech tracking of degraded speech has been used to advance the understanding of how brain processes and speech intelligibility are interrelated. However, the temporal dynamics of neural speech tracking and their relation to speech intelligibility are not clear. In the present MEG study, we exploited temporal response functions (TRFs), which has been used to describe the time course of speech tracking on a gradient from intelligible to unintelligible degraded speech. In addition, we used inter-related facets of neural speech tracking (e.g., speech envelope reconstruction, speech-brain coherence, and components of broadband coherence spectra) to endorse our findings in TRFs. Our TRF analysis yielded marked temporally differential effects of vocoding: ∼50–110 ms (M50TRF), ∼175–230 ms (M200TRF), and ∼315–380 ms (M350TRF). Reduction of intelligibility went along with large increases of early peak responses M50TRF, but strongly reduced responses in M200TRF. In the late responses M350TRF, the maximum response occurred for degraded speech that was still comprehensible then declined with reduced intelligibility. Furthermore, we related the TRF components to our other neural “tracking“ measures and found that M50TRF and M200TRF play a differential role in the shifting center frequency of the broadband coherence spectra. Overall, our study highlights the importance of time-resolved computation of neural speech tracking and decomposition of coherence spectra and provides a better understanding of degraded speech processing.