What is causing my '02 Grand Prix to shift so hard?

You've already let it go too long. If the transmission is slipping you've pretty much finished it off. Check the fluid. Is it full? Does it smell burnt? If its down fill it up and it may go a few more weeks. There are also some electronic components that can fail so take it to a shop and have that checked out, but prepare for the worst.

@munron It isn't too common of a thing, I notice it does this when I don't let it warm up enough in the morning. Even then, it only does weird shifts only once or twice. When I first got the car my stepdad (who's a mechanic) checked the trans fluid and said it was overfull and that helped a bit. I have another exhaust problem, the flex pipe, and I got the parts to fix that

Sounds like the transmission might not be as far gone as I thought then. Still it sounds like its on its way out an these things always get worse, never better. Start looking for a used one you can put in. It's not worth the expense of getting it rebuilt.

@munron Thanks a lot, my step-dad is a mechanic and does all of the work on my car. He's been pretty busy lately with others trying to get their cars ready for spring but I want a good idea of what needs to be done so I know what expenses I need to put aside.