The influence of turbulence on the spectrum of diffracted chirped Gaussian pulsed beams is studied in detail. By using the quadratic approximation of the Rytov's phase structure function and the finite expansion of the aperture function, the analytical expression for the spectrum of diffracted chirped Gaussian pulsed beams propagating through atmospheric turbulence is derived. It is shown that in free space there exist the on-axis and off-axis multi-spectral switch for diffracted chirped Gaussian pulsed beams. However, the turbulence results in a decrease of the spectral transition height, and the spectral switch even disappears when the turbulence is strong enough, which is very different from the behavior of undiffracted chirped Gaussian pulsed beams. Specially, with increasing the strength of turbulence, the higher-order spectral switch disappears firstly for on-axis case, while the lower-order spectral switch disappears firstly for off-axis case. In free space the on-axis spectrum is blue-shifted after a certain propagation distance, but the on-axis spectrum is red-shifted after a shorter propagation distance when the turbulence is strong enough. The spectral transition height increases with increasing the chirp parameter and decreasing the pulse duration, and the odd number order position without spectral shift is independent of the chirp parameter and pulse duration.