Atticus is trying to demonstrate that Bob Ewell, not Tom Robinson, is the one who beat Mayella.
At the trial, Atticus questions Mayella and Bob, trying to establish that Mayella’s injuries are consistent with her father’s physical characteristics, not Tom Robinson’s.
Atticus was trying to show, it seemed to me, that Mr. Ewell could have beaten up Mayella. … If her right eye was blacked and she was beaten mostly on the right side of the face, it would tend to show that a left-handed person did it. (ch 17)
Tom Robinson’s injuries prevent him from being able to attack Mayella. Even though he is strong, he is crippled. Atticus wants to show the jury that Tom Robinson did nothing, and that indeed no crime even took place.
Although Atticus’s logic is easy to follow, the jury does not acquit him because they cannot take a black man’s word over that of a white woman.