The propagation equations of second-order moments of truncated circularly symmetric beams are derived, which obey the propagation laws similar to those for the non-truncated case. Based on the method of generalized truncated second-order moments, the second-order characteristic parameters of two-dimensional truncated beams in the rectangular coordinate system are extended to the truncated circularly symmetric beams in the cylindrical coordinate system, and the generalized M2 factor (M2G factor) can be defined in a similar way and remains invariant upon propagation. The consistency of the theory is interpreted physically. The second-order moments parameters and M2G factor of truncated super-Gaussian beams in the cylindrical coordinate system are derived and some interesting special cases are discussed and illustrated with numerical examples.