In a small bowl, combine the vegetable oil, salt, dry mustard, paprika, and hot sauce. Stir until well blended and set aside.
Separately, combine 1/2 cup of the grapefruit juice and cornstarch in a small saucepan and stir to blend. Stirring constantly, cook over medium heat until the mixture is bubbly and thickened. Remove from the heat.
Combine the oil and cornstarch mixtures in the bowl and then beet with an electric mixer at medium speed until smooth. Add the remaining 1/2 cup of grapefruit juice and beat until the dressing is blended well.