Using a total of 11.0 fb^{-1} of e^{+}e^{-} collision data with center-of-mass energies between 4.009 and 4.6 GeV and collected with the BESIII detector at BEPCII, we measure fifteen exclusive cross sections and effective form factors for the process e^{+}e^{-}→Ξ^{-}Ξ[over ¯]^{+} by means of a single baryon-tag method. After performing a fit to the dressed cross section of e^{+}e^{-}→Ξ^{-}Ξ[over ¯]^{+}, no significant ψ(4230) or ψ(4260) resonance is observed in the Ξ^{-}Ξ[over ¯]^{+} final states, and upper limits at the 90% confidence level on Γ_{ee}B for the processes ψ(4230)/ψ(4260)→Ξ^{-}Ξ[over ¯]^{+} are determined. In addition, an excited Ξ baryon at 1820 MeV/c^{2} is observed with a statistical significance of 6.2-6.5σ by including the systematic uncertainty, and the mass and width are measured to be M=(1825.5±4.7±4.7) MeV/c^{2} and Γ=(17.0±15.0±7.9) MeV, which confirms the existence of the J^{P}=3/2^{-} state Ξ(1820).