Blending a smoothie without changing the taste
You actually made me look up „smoothie“ because I wanted to double-check for some kind of definition.
^_^

Your current ingredient list is 


Mango, frozen 
Ice cubes


If you throw that in a blender (provided yours is powerful enough, many are), you get some kind of ice slush - like a frozen smoothie. The trivial suggestion would be to use water instead of ice (substituting all or some of the ice cubes), but you ruled that out as tasting too watery - unless this already solves your problem. Using (softened/thawed) mango alone will probably be too thick, but it’s a matter of taste.

Personally, I am not the greatest fan of adding plain water or too much ice, simply for the reasons you stated: it can be a too prominent taste, especially if the water isn’t “tasteless” from the beginning, which is the case in some places of the world, either because it’s chlorinated or very mineral-rich, or it can dilute the fruit flavor. My standard approach is to use parts whole fruit, parts juice, either from the same fruit or something  that goes well together. The options are endless and I feel smoothies are a good area for experimenting with flavor combinations. If you feel adventurous and don’t like dairy, you may consider coconut water as liquid, for example.