Mix ¼ c juice with 3 T cornstarch until there are no lumps. Set aside.
Mix sugar, vinegar, salt, and rest of beet juice; whisk while bringing to a boil. Add beets and heat until beets are hot. Re-mix the juice/cornstarch and pour in, continuing to whisk. Continue cooking, whisking, until sauce is thick.
Add more water if sauce is too thick.
If sauce is too thin, mix some more cornstarch with water. Start with 1 T in about 2 T water. Pour in, whisking.
Add butter last, if using.
Harvard beets are wonderful with pork chops! My sister and I asked Mama to make this often, and she obliged, pan-sautéeing the meat. One dips a bite of pork into the beet sauce! Yum! (Don't overcook the pork; it should not be tough and dry.)