Poor Primitivo. There's just not a whole lot to say about him, besides the fact that he's got a flat face and is getting on in years. He gets stuck being called "flat-faced Primitivo," or "the flat-faced man" all the time. It's an epithet, you might say, kind of like "Hector, breaker of horses" in the Iliad.
Primitivo is a pretty dependable, but average, member of Pablo's band, a guy who kind of moves with the herd. He gets a fair amount of action, serving as the sentry when Robert Jordan and Agustín lie in wait for the patrol, and fighting at the bridge, of course, all the while without particularly distinguishing himself. Maybe that's why he seems to want to play the hero and go to the aid of El Sordo when he gets attacked, dying in the process.
Well, we suppose if we want to find the "deeper purpose" of Primitivo's character, it's contained in that episode: Primitivo is somebody who hasn't yet accepted the brutal and very un-romantic reality of war, where you do have to let your best friends die if you want effectively to serve your cause. He's a different kind of "idealist" (someone with noble illusions which are untrue to reality) than "Robert Jordan the fanatic" was in days of yore, though. Robert Jordan was all about the cause, and Primitivo is all about his friends.