In a small saucepan, bring the water to a boil with the sugar and jalapeño, stirring to dissolve the sugar. Let cool completely, then strain the syrup; discard the jalapeño.
In a large pitcher, combine the jalapeño syrup, pineapple juice and sake and stir well. Refrigerate until well chilled, about 1 hour. Serve the sangria over ice in tumblers, garnished with pineapple and mint.