If you want to blend ice smoothly, then odds are you're looking to create a slushy type drink in the comfort of your own home. Many people run into issues when trying to put ice cubes in their blender because they notice that it doesn't come out quite like it does from a convenience store or when you get a frozen drink from a shop.
Here are three different ways that I like to create a drink that has the texture of smoothly blended ice
Add the Ice Slowly
If you add the ice to your blender all at one time then odds are you're going to get things clogged up. By blending your liquid and adding the ice a few cubes at a time or in different phases and you'll have a much easier time getting a smooth slushie like texture.
When you when you do this you'll notice that the liquid in the blender will turn into a cyclone and draw everything towards the blades. This is what you want if you truly want your ice to be smooth and not in chunks.
Make sure that before you add new cubes that the previous round of ice cubes you threw in where appropriately homogenized with whatever you are blending.