Recently, three major types of minima (i.e., Cooper-like minimum, two-center interference minimum and multi-channel interference minimum) have been observed in high-order harmonic generation (HHG) spectra. Identification of the origin of the minimum in a HHG spectrum is critical for self-probing of the molecular structures and dynamics, which has been an important subject in attosecond physics. In this paper, we report the investigation of the multi-electron dynamics in HHG from N2 molecules driven by intense mid-infrared laser pulses. Based on a pump-probe experimental setup, clear spectral minima in the cutoff region of high harmonic spectra from N2 molecules are observed in measurements with mid-infrared laser pulses at three wavelengths (i.e., 1300, 1400 and 1500 nm). A systematic investigation has been carried out for clarifying the origin of these minima. We carefully measured the spectral minima under three different experimental conditions:1) different alignment angles of molecules; 2) various peak laser intensities; 3) tunable driving laser wavelengths. Experimental results show that the positions of the spectral minima do not depend on the alignment angles of molecules. In addition, the measured spectral minima shift almost linearly with the laser intensity for all three wavelengths, and the positions of the spectral minima strongly depend on the wavelengths of the driven field. These findings are in conflict with the Cooper-like and two-center interference minima predictions, providing strong evidences on the dynamic multi-channel interference origin of these minima. Besides, we theoretically calculated the positions of multi-channel interference minima by using a classical three-step model and found out perfect agreements between the experimental results and theoretical calculations, which again strongly support the multi-channel interference picture. Moreover, the advantages of the observed dynamic multi-channel interference based on HHG driven by long wavelength lasers are discussed. The long wavelength driver lasers are attractive for not only generating coherent XUV radiation and attosecond pulses, but also investigating structures and dynamics of molecules in strong laser fields.