At one side you said it is not a mixer and while on the other hand, you said, it's a wallet with mixing capabilities

Do you mean to say that we can mix our coins through this wallet and may not need a external mixer ?
The name of the safe reflects the name of the parent company "Mixin Ltd" from Hong Kong. They do not provide bitcoin mixing service for people who want to mask the origin and destination of their coins, do not get it confused.
Mixin safe
is designed to offer enhanced security for digital investments, and Mixin Ltd doesn't hold any assets belonging to its customers.
source