We show that the asymptotic dynamics of two-dimensional de Sitter or anti-de Sitter Jackiw-Teitelboim (JT) gravity is described by a generalized two-particle Calogero-Sutherland model. This correspondence is established by formulating the JT model of (A)dS gravity in two dimensions as a topological gauge theory, which reduces to a nonlinear 0+1-dimensional sigma model on the boundary of (A)dS space. The appearance of cyclic coordinates allows then a further reduction to the Calogero-Sutherland quantum mechanical model.