If by "mean" you meant scary or terrifying "game face", here is a list by position, of some candidates.
In reverse position order:
1. RF. Carl Furillo, Dave Parker, Albert Belle,
2. CF. Ty Cobb and he is my # 1 as a scowling terror at bat or on the base-paths.
3. LF. Jim Rice, Barry Bonds, and Charlie "King Kong" Keller.
4. SS. Best game face was Barry Larkin, but not particularly scary.
5. .3B. No candidates, but any time Mike Schmidt or George Brett had a bat in their hands, pretty scary.
6. 2b. Rogers Hornsby, Joe Morgan, or Jackie Robinson.
7. 1B. Jimmie Foxx, a holy terror.
8. C. Thurman Munson or Ernie Lombardi.
9. P. So many. From the 1900's, Eddie Plank. From the 1920's, Carl Mays. From the 1930's, Lefty Grove. From the 1940's and early 50's, Sal Maglie. 50's, 60's, and 70's, Don Drysdale, Ferguson Jenkins, and Bob Gibson. From the 1980's and 1990's, Steve Carlton.
Of the 2000's, Jonathan Broxton.
All time, pitcher game face is Dave Stewart of the Oakland A's, from the 80's and early 90's.
His cold glare at hitters, earned him the nick name of "Dr. Death".