You'd need a very, very big explosive for any but the smallest grains to have divergent paths. They would form a cloud of debris that would travel on the same orbital path but spread out a bit. Breaking an asteroid up only works if it's fairly small to begin with since anything over about 50 meters that is solid is still going to be dangerous. If you broke a 2km asteroid into a mixture of 50m to 100m chunks of solid rock or metal then you're still going to have a very bad time when all that debris obliterates a state or small country.