I work part-time at a warehouse in missouri. They told me that overtime is mandatory. I got wrote up for clocking out after working a 9 hour shift. Can they make me work overtime if I'm just a part-time employee?

Yes, they can. With a very few industry specific exceptions where public safety is involved (airline pilots, truck drivers) mandatory overtime is legal in all 50 states. No law in any state limits it to only full time employees.