Tip the pineapple pieces into a food processor with their juice and blitz to a purée. Pour into a pan and add the caster sugar and 200ml water. Stir over a low heat until the sugar has dissolved.
Take off the heat and stir in the lime juice and coconut milk. Transfer to a measuring jug and add enough cold water to make it up to 1 litre. Leave to cool.
Pour into a freezer-proof container and freeze for 2 hours, or until just set. Tip the mixture into a bowl and whisk with an electric beater for a few minutes, until smooth. Pour back into the container and freeze overnight.
Break up with a fork and serve in glasses. Decorate with washed raspberries and mint leaves.