Yes you can eat sweet potato skin.
Sweet Potato Skin is edible just like other potato skins are edible.
The potato skin on both sweet potatoes and regular potatoes provide you with many health benefits because the sweet potato skin and regular potato skin contain vitamins, minerals, nutrients etc.
Eating the skin of the sweet potato will provide you with more health benefits than just the sweet potato alone.
I love eating the skin of sweet potatoes along with the sweet potatoes themselves.
There's no need to throw the sweet potato skin away or any other potato skin as they are very nutritious and healthy.