1. Cut ends from prickly pears. Cut a 1/8-inch-deep lengthwise slit through peel on each fruit. Pull back peel and remove from pulp; discard peel. Cut fruit pulp into 1/2-inch chunks.
2. In a blender, combine half of all these ingredients: prickly pear chunks, lime juice, tequila, orange liqueur, and sugar; whirl until smooth. Add half the ice and whirl until blended. Pour into glasses slowly, leaving seeds behind. Discard seeds.
3. Repeat step 2 with remaining pear chunks, lime juice, tequila, liqueur, sugar, and ice.
4. Garnish with lime slices.
Look for prickly pears (also called cactus pears, Indian figs, and tunas) with fresh produce in supermarkets and Latino markets. Wear heavy cotton or rubber gloves or use a thick towel to hold them when peeling.