Is it legal for my company to not reimburse me for mileage and parts and why?

I know of no law in Georgia that required employer to pay you for this. Many jobs require personal use of vehicles. Add your pay and your car expenses together. Divide by number of hours you work. That gives you a hourly rate you are being paid, after adding in the car expense. If that number is less than minimum wage, you may have a claim against the employer. if it is more than min wage, I suspect completely legal. Your remedy is to negotiate a change, or accept this, or find another job. If you are not in GA, resubmit your question, and identify your state. for more info, google this: Georgia, employment at will.

I do not understand your mileage and "parts". Generally, you are paid or reimbursed by your employer in accord with your agreement with them. They do not have to reimburse you for the personal use of your automobile unless there is an agreement or company policy to do so.