Preheat the oven to 250°F (121°C). Line 2 large rimmed baking sheets with parchment paper.
Using a mandoline or a sharp knife, slice the vegetables evenly about 1/8 inch (3 mm) thick. Place the beet slices in a medium bowl and the sweet potatoes in another medium bowl.
Add 1 tablespoon olive oil and 1/2 teaspoon salt to each bowl and toss.
Spread the beets in a single layer on 1 of the baking sheets and the sweet potatoes on the other, being careful not to let the slices overlap.
Bake the root vegetable chips, rotating the pans after 1 hour, until crisp, 1 hour, 40 minutes to 2 hours for the sweet potatoes and 1 hour, 50 minutes to 2 hours for the beets.
Transfer the chips to a large bowl and serve immediately. (In the unlikely event you have leftovers, they’ll keep for up to 3 days in an airtight container.)