We have analyzed the effect of axial guiding magnetic field on the wave dynamics in plasma-beam superheterodyne free electron laser (SFEL) of the Dopplertron type with helical relativistic electron beam in the framework of cubic nonlinear theory. We have found the magnetic field critical values and the saturation levels. We found out that the saturation level of electromagnetic waves is maximal at a certain value of the longitudinal magnetic field strength (the magnetic field critical value). We demonstrated the possibility of a plasma-beam SFEL to generate powerful electromagnetic radiation in the millimeter wavelength range.