Slice cucumber in half lengthwise, then slice in diagonal 1/4-inch-thick slices.
In a small bowl, whisk together the lime juice, fish sauce, sugar, crushed red pepper, and shallot. Add 3 tablespoons water, and whisk until the sugar is dissolved.
Place the cucumber and pineapple on a serving platter, and drizzle with some of the dressing. Arrange the roast beef on top and place the mint sprigs alongside. Serve, passing the remaining dressing at the table.