What can I do if I have a massive personal problem with a future student?
the nature of the problem is that the student violently assaulted my girlfriend [...] Charges were filed and I stand by the seriousness of the accusation.


The fact that there is a criminal case involved makes this situation much more serious than just disliking someone. It doesn't matter whether you think you could behave impartially or not, the appearance of a conflict of interest is what is important, and that is most certainly present here. If the student is doing poorly, the student could accuse you of unfair treatment regardless of your behavior, and there would most likely be an investigation. It's better to avoid that possibility entirely.

You need to talk to your professor immediately. Depending on the status of the case, tell your professor that your girlfriend and the student are on opposite sides of a criminal case. This should convey the seriousness of the conflict without disclosing too many personal details. Keep in mind that there are privacy issues with saying too much about your student's personal life, in particular when it comes to criminal charges.

Work with your professor to figure out what the best solution is, whether that means switching sections with another TA, switching the student to another section, or putting in place defined procedures to prevent bias on your part (such as anonymous grading). It may be a good idea for your professor to involve an ethics adviser from the university, since the conflict of interest is so clear. Regardless of the outcome, by officially reporting this potential issue ahead of time, this will reflect positively on you in the event that the student does make any complaints.