I encounter dumb struck much more often than struck dumb, but people still sometimes use struck dumb. They can also be used for negative emotions, people can be "dumbstruck with terror" for example.

Dumbstruck isn’t very commonly used in the US and I’ve never heard anyone say “struck dump”. A much more common word that means the same as dumbstruck would be “speechless”, for example: The rudeness of that jerk left me speechless. Or, The beauty of the Grand Canyon left me speechless. Or, To say that I was speechless at the generosity of your gift is an understatement! I will say that “dumbstruck” is more an expression of astonishment (in a negative way) than “speechless” (which can be used in either a negative or a positive context) would be. I hope I have been of some help!

Agree with Dusan. You would generally hear people say dumbstruck as opposed to struck dumb. The term would normally imply a negative emotion rather than a positive one.