Place raspberries and sugar in a large heatproof jug and stand for 10 minutes, stirring occasionally, until sugar has dissolved.
Meanwhile, place teabags in a separate heatproof jug, add 1L boiling water and steep for 5 minutes. Add peppermint tea to raspberry mixture and gently stir. Strain, reserving a few raspberries and set aside to cool to room temperature.
Add spearmint leaves and chill. Serve cold with reserved raspberries and crushed ice.