I love fruity drinks so have started freezing fresh fruit that needs using up, I freeze strawberries, apples, oranges, lemons, melon. limes, grapes, pears & even bananas, I then just chuck few frozen fruits into a jug & fill with fruit juice, there's no need to add ice as the frozen fruits act as ice cubes, plus they don't dilute the drink like ice cubes do.
I have a centrifugal juicer which is ideal for juice, but you can make a sorbet if you mix the pulp residue with the juice and freeze it. [If I juice vegetables Pereg gets the pulp residue - no waste chez Malka! ] Another way of making a fruit sorbet is to use an electric mincer if it has a sausage nozzle.