If I'm understanding you correctly, the gap you have god filling is the "natural" in selection. The arbitrary mutations side is something "designed" that runs on its own in the way we observe, but the actual removal of the "unfit" varieties is a direct intervention from on high. Yes?
This isn't bad theology, really. The Bible and world mythology are pretty much in agreement that the main activity of deity is to destroy person, places and things.
But to be science there has to be a way to falsify your hypothesis.
How can sceintists accept a belief
Here I think is where you are going wrong.
Belief is for losers. The reason science is a winner is because, instead of believing the things its imagination poops out, it immediately begins trying to come up with ways to disprove these things.
So, what predictions could we make based on your idea that it's god killing mammoths and leaving elephants alone, or whatever example suits you. What experiments can we do to test these predictions. What results would falsify your theory?