To overcome the low efficiency of conventional confocal Raman spectroscopy, many efforts have been devoted to parallelizing the Raman excitation and acquisition, in which the scattering from multiple foci is projected onto different locations on a spectrometer's CCD, along either its vertical, horizontal dimension, or even both. While the latter projection scheme relieves the limitation on the row numbers of the CCD, the spectra of multiple foci are recorded in one spectral channel, resulting in spectral overlapping. Here, we developed a method under a compressive sensing framework to demultiplex the superimposed spectra of multiple cells during their dynamic processes. Unlike the previous methods which ignore the information connection between the spectra of the cells recorded at different time, the proposed method utilizes a prior that a cell's spectra acquired at different time have the same sparsity structure in their principal components. Rather than independently demultiplexing the mixed spectra at the individual time intervals, the method demultiplexes the whole spectral sequence acquired continuously during the dynamic process. By penalizing the sparsity combined from all time intervals, the collaborative optimization of the inversion problem gave more accurate recovery results. The performances of the method were substantiated by a 1D Raman tweezers array, which monitored the germination of multiple bacterial spores. The method can be extended to the monitoring of many living cells randomly scattering on a coverslip, and has a potential to improve the throughput by a few orders.