The problem with a true beater is that it is likely to cease working pretty soon, unless you keep parts updated when necessary. For most commuters, it might mean having an older bike that is upgraded to be functional.
For my mind, a beater is a bike you could press into service as a winter bike or one that wouldn't tear your heart out if stolen...
The OP's Rockhopper might be a beater in someone's eyes, but seems like a pretty nice bike to me.