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Ah...surely the bigger question how can we do it? 
Another application for a vacuum cleaner. Sorry to recycle this joke.If you mean to make it magically disappear I guess the effect would be to make the unverse expand more quickly. Dust makes up a significant perentage of the total visible mass but not much of the total mass, so I guess the effect may be small. However we do not understand very much about the balance of mass vs dark energy and so maybe it could have significant effects if mass were suddenly to disappear. I am not sure that such a hypothetical, and impossible, idea has much value except to a zen physicist :-)