In this paper, we consider the quasilinear fractional reaction-diffusion equation with singular potential the existence, decay estimate and long time asymptotic behavior of the global solution and the blowup behavior of the solution are discussed. Because of the non-locality of fractional Laplacian operator, the Caffarelli-Silvestre extension method is used to transform the nonlocal problem into an elliptic problem with dynamic boundary conditions. Firstly, the global existence of the solution is proved under appropriate assumptions, and on this basis, the decay estimate and long time asymptotic behavior of the global solution and the blow-up behavior of the local solution are obtained by using the potential well methods.