"There are mice here."
It isn't if the sentence is said with a proper intonation - the entire pitch fall should be on мыши, bringing the word to the listener's attention as carrying new information. But if pronounced with a neutral intonation where the pitch doesn't fall until the last word, the sentence will be understood as "The mice are here"
I'm guessing here, but I think in that sentence the emphasis is on "mice" as usually the thing we are sure about or the definite object comes first. so Мыши здесь. would be more like "the mice are here" whereas Здесь мыши. would be more like "Here are mice".
So in "There are mice here", we are aware of "here" and that is definite, but the mice are a new thing that we are pointing out. If we were already talking about the mice then you could say "Мыши здесь" ie "the mice are here"
You'd say "Здесь мыши" (1) to explain why you don't like the place or (2) while giving someone a tour of a zoo or a room where you keep your pets, to inform the person(s) about the species kept in a particular place. You'd say "Здесь есть мыши" to inform someone of the presence of mice in the place.
The rule of thumb is: if the English sentence starts with “There is” / “There are” etc., the equivalent Russian sentence should start with the adverbial modifier of place. With neutral intonation, «Мыши здесь» means “The mice are here”, and if you emphasize «мыши» by saying «МЫШИ здесь», the meaning will change to “It’s mice that we have here, [rather than any other kind of rodents]”.