In a large saucepan, combine the sweet potatoes with the cider and water and bring to a boil. Simmer over moderate heat until the sweet potatoes are just tender, about 35 minutes. Drain in a colander and shake dry.
In the same large saucepan, bring the butter and maple syrup to a boil. Add the potatoes and toss. Working in batches, puree the sweet potatoes in a food processor; do not overprocess. Season with salt. Return the whipped sweet potatoes to the saucepan and heat over moderate heat until warmed through, about 10 minutes.