Tom

"Ain't nigger enough in him to show in his finger-nails, en dat takes mightly little-- yit dey's enough to paint his soul." (76).

Roxy blames the way in which Tom can act so poorly towards others and ungentlemanly on the fact that he isn't fully white. This is an idea the reader has to wonder if Twain is trying to put out there. Is Twain saying that no matter how a black person is raised, they will act badly? No. And here lies the beauty in the craft of Twain's writing.
Twain contrasts this idea against the other characters such as Roxy and Chambers.
Roxy, a women is also mixed with white and black descent, is willing to be sold back into slavery for the good of her child. She does everything in her power to do what's best for him and hates to see him suffer.
Tom is also compared against Chambers. Chambers is completely white and yet raised as a slave. Yet we see Chambers is stronger, kinder, and overall better than Tom. This once again, isn't making the statement that black is inherently bad and white is inherently good, but instead shows that the meekness in which a slave is raised and the spoiled way in which a rich white is raised is what makes them different. It isn't an issue of race at all.