Stimulus response of polymer-decorated nanopores/nanochannels is a fascinating topic both in polymer science and modern nanotechnology; however, it is still challenging for standard analytical methods to characterize these switchable nanopores/nanochannels. In this study, based on the physics of polymer translocation, we developed an analytical method and thus for the first time were able to quantitatively measure the effective thickness of the polymer layer around the rim of nanopores. As an application example of this method, we studied the translocation dynamics of fluorescence DNA through poly(Nisopropylacrylamide)-decorated switchable nanopores in aqueous environments. By adding small amounts of ethanol to the aqueous buffer solution, a switch-like response of the DNA translocation can be observed. It is also observed that a pronounced switching effect can be only realized in a window of moderate grafting densities of the poly(N-isopropylacrylamide) layer. These are attributed to the cononsolvency effect which causes a collapse of the polymer layer and thus a transition between "closed" and "open" states of the nanopores for DNA translocation. Our study clearly transpired that the cononsolvency effect of polymers can be used as a novel trigger to change the size of nanopores, in analogy to the opening and closure of the gates of cell membrane channels. We envisage that our study will spawn further developments for the design of switchable nanogates and nanopores.