This paper explores the influences of the rotational speed on the dynamic stability of the sandwich truncated conical shells (STCSs) with graphene platelets (GPLs) reinforced porous core and face sheets (GPLR-PC-FS) subjected to harmonically time varying normal stresses on their edges. The motion equations, which include Coriolis force and the induced mechanical stresses due to angular speed of the shell, are derived based on the first-order shell shear deformation theory. The differential quadrature method (DQM) in conjunction with the Bolotin method are utilized to estimate the instability regions of the rotating STCSs with GPLR-PC-FS. By displaying its fast convergence rate and different verification examples results, the approach is validated. In continuation, by conducting parametric studies, the influences of angular speed, porosity distribution and amount, weight fraction of GPLs, boundary conditions and geometric parameters on the stability behavior of the rotating STCSs with GPLR-PC-FS are explored. The results show that the increase of the shell rotational velocity, increases the shell unstable regions and it occurs at lower exciting frequencies. Also, the increase of GPLs weight fraction, and interestingly the increase of pores, improves the dynamic stability behaviors of the rotating STCSs with GPLR-PC-FS.