To make frosting, beat cream cheese on low speed in the bowl of a stand mixer fitter with the paddle attachment or a large mixing bowl for 3 minutes. Add the butter and beat 3 minutes more, scraping down sides as needed. Sift in powdered sugar, add sea salt, and beat 4 minutes longer, scraping down sides as needed. Add blood orange juice and zest, and beat until well incorporated. Add beet juice a little at a time, until the desired color is achieved.