The molecular dynamics of an ionic liquid (IL) composed of a 1-ethyl-3-methylimidazolium cation and a triflate (trifluoromethanesulfonate) anion, abbreviated as [Emim][TfO], were studied by NMR spectroscopy. By measuring the temperature-dependent high-field 1H and ¹⁹F spin-lattice relaxation (SLR) rates, the frequency-dependent ¹H and ¹⁹F SLR dispersion curves using fast-field-cycling relaxometry, and the temperature-dependent 1H and ¹⁹F diffusion constants, and by utilizing the fact that the primary NMR-active nucleus on the Emim cation is ¹H, whereas on the TfO anion it is ¹⁹F, the cationic and anionic dynamics were studied separately. A single theoretical relaxation model successfully reproduced all the experimental data of both types of resonant nuclei by fitting all the data simultaneously with the same set of fit parameters. Upon cooling, [Emim][TfO] exhibited a supercooled liquid phase between T_SL = 256 K and the crystallization temperature T_Cr ≈ 227–222 K, as confirmed by differential scanning calorimetry (DSC) experiments. Theoretical analysis revealed that within the liquid and the supercooled liquid states of [Emim][TfO], the ¹H and ¹⁹F relaxation rates are affected by both the rotational and translational diffusional processes with no discontinuous change at T_SL. While the rotational diffusion is well described as an Arrhenius thermally activated process, the translational diffusion undergoes strong freezing dynamics that are well described by the Vogel–Fulcher model assuming a freezing temperature of T₀ = 157 K. The existence of the supercooled liquid region in the [Emim][TfO] IL should be taken into account when using this IL for a specific application.