What exactly is a mop-up guy? The technical term is a long reliever and they're usually brought out of the bullpen for more than a few innings. However, if they're primarily brought into the game when the chances of victory are slim, they've been unofficially demoted to being the mop-up guy. More often than not, these roles are held by pitchers with the stamina and arsenal to be starters but without the stuff to be trusted every five days.
Cooper Criswell, who the Mariners acquired for cash last week, fits that definition.