I would say that Tea Cake is acting within an aspect of his character—particularly that which has developed out of internalized racism.
Mrs. Turner is a woman who tries to befriend Janie. She is Janie's and Tea Cake's neighbor in the muck—the farm in the Everglades where they have gone for work—and makes a point of disrespecting Tea Cake due to his darker skin. Mrs. Turner encourages Janie to date her (Mrs. Turner's) brother, instead, because he is lighter-skinned. Tea Cake's awareness of this exchange makes him fear that he will lose Janie, who is also lighter-skinned. This fear in Tea Cake suggests that he, too, thinks that lighter-skinned people are better. He beats Janie in a perverse way of showing the Turners—and Janie—that he is in possession of Janie. This behavior is not necessarily stereotypical of black men, as the previous Educator notes, but stereotypical of men in general, who sometimes use women as the accessories of their power.
In having Tea Cake beat Janie, Hurston reveals the complexity of his character and that of many men. Tea Cake loves Janie, but he is willing to hurt her because his pride has been hurt. This causes the reader to question the nature of love and how certain societal forces—sexism and racism—devalue the love between people.