Can you still tumble with a mild ankle sprain?

You can, but if you want your ankle to heal quickly then you really should rest it. A sprain is painful, and tumbling will hurt. Plus depending on the intensity of your tumbling, some tumbling (like back-handsprings or tucks) require the tumbler to have strong ankles. When your ankle is sprained, it is not at its full strength. So you need to be careful, because tumbling with your sprained ankle could lead to more injuries. I really suggest that you rest your ankle, put as little weight on it as possible, use ice and heat when needed, wrap it, and give it time. When the pain and swelling goes down a little, start tumbling little by little. You'll be back to tumbling in no time, though, so don't worry. A sprain takes much less time to heal than a fracture does.