So in my experience, the key to a good knock-off frapp is two things:
1) a really really good blender - I use a VitaMix, you could also use a BlendTec
I tried using my old Oster blender, and it's just not the same. It doesn't break the ice down into small enough pieces to get that velvety, milkshake/smoothie-like texture. The texture is a large part of the frapp "experience" and it won't be right if you don't use the same type of blender.
2) Xanthum gum. I get mine from the baking aisle at Whole Foods - it's about $12 for a bag with a cup or a cup and a half in it. I use it up 1/4 t at a time, so one bag will last a really really long time.
Here is a recipe for a homemade frapp that is a pretty good imitation. For a mocha frapp light, you should sub sugar-free chocolate syrup for the sugar and experiment from there.