Mussels do not have brains like humans and most other animals do.
Mussels do however have nerves which allows the mussel to feel pain and move around.
Other things besides mussels that have no brains are oysters and clams but they do all have nerves.
However mussels while they do have nerves the mussels and clams and oysters have no central nervous system or brain.
But oysters, mussels and clams can feel pain.
So when you do kill the mussel or oyster or clams they do feel the pain but not the same pain we humans and other animals feel.
They feel like a tingling sensation when you harm them, cut them or kill them.