Here's why:
* "Le style" means "the style".
* "Du mime" means "of the mime".
Together, they create a phrase that clearly conveys the meaning of "mime style".
You could also use "le style mimique" which literally translates to "the mime style".
However, it's worth noting that "mime" is already a noun in French, so it's more natural to use "le style du mime" to emphasize the style associated with the act of mime.