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.
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.
Repeat step 2 with remaining pear chunks, lime juice, tequila, liqueur, sugar, and ice.
Garnish with lime slices.