Dynamic biochemical signal control is important in in vitro cell studies. This work analyzes the transportation of dynamic biochemical signals in steady and mixing flow in a shallow, Y-shaped microfluidic channel. The characteristics of transportation of different signals are investigated, and the combined effect of transverse diffusion and longitudinal dispersion is studied. A method is presented to control the widths of two steady flows in the mixing channel from two inlets. The transfer function and the cutoff frequency of the mixing channel as a transmission system are presented by analytically solving the governing equations for the time-dependent Taylor-Aris dispersion and molecular diffusion. The amplitude and phase spectra show that the mixing Y-shaped microfluidic channel acts as a low-pass filter due to the longitudinal dispersion. With transverse molecular diffusion, the magnitudes of the output dynamic signal are reduced compared to those without transverse molecular diffusion. The inverse problem of signal transportation for signal control is also solved and analyzed.