Hmm, I don't think I've heard of anyone on here juicing veggies. Most people can't go raw veggies because they're hard to digest; juicing may be a good alternative to get the vitamins and other good things, without getting all that insoluable fiber that some people's bodies just don't process too well.
Sweet potatoes are almost as hard raw as a white potato, so I would think that you would need to cook them first before putting them in the blender. However, I don't know that sweet potatoes will "juice". Beets have a lot of moisture, but I would think that a sweet potato would just become a sweet potato puree. Anyways, bake them in a microwave or oven because when you boil something, some of the vitamins will leech out into the boiling water and get thrown away. Cook with the skin on to keep the juices in as much as possible, then yes, peel before you grind it up. While potato peels are supposed to be good for you, I don't think they'd drink too well!
I don't know if you're also doing fruit juice, but a LOT of people on here have trouble with fruit juices. I think apple juice is pretty much universally a problem. Apple juice is something of a natural laxative anyways (although in people with C it just seems to give them worse gas and cramping), but in other fruits it seems that the acid is probably the major source of the problem (gas, cramping, D). You might want to stay away from fruit juices or at least mix them in with vegetable juices to cut down on them. Cooked fruits, however, seem to be better tolerated. Bananas are one of the few fruits without acid in them, and they are a natural constipator--good if you get D, not good if you are prone to C!