Daiquiri refers to a cocktail which is traditionally prepared with rum, lime juice, and sugar. Daiquiris are also made with fruits. Frozen Daiquiris are made by adding crushed ice and fruit chunks and pureeing them in a blender until smooth for a thick frothy version Daiquiri was invented by an American mining engineer working near the town of Daiquiri in Cuba and is named after Daiquiri, a rum-producing town on the east coast of Cuba.