Wash the peeled and chopped potatoes well under cold running water. Add them and salt to a large pot and cover the potatoes with cold water. Bring to a boil and cook until potatoes are fork-tender. Drain and set aside to cool slightly.
Using a hand-held potato masher, or a potato ricer, mash the potatoes leaving no lumps.
Add all of the other ingredients, except for 1/4 cup of the beet juice, and using a large spoon, vigorously mix all of the ingredients together.
Taste for seasoning and sweetness and adjust accordingly. Add more beet juice if you would like a deep pink potato salad, but only add the extra beet juice if the potato salad is not already too moist.
Transfer to a glass bowl with a tight fitting lid. Refrigerate for at least 4 hours or overnight for best results.