I'm going to tell my roommate to clean her room or I will move out
Why do you want to tell her this?
Her room is always a mess.
If your roommate is being messy then you have the right to tell them to clean up. You live there too so any rodents or pests they attract will go to your room as well.
I'm also considering just taking her stuff and throwing it away if she doesn't want to clean.
I think it's okay to expect your roommate to have a clean room but throwing her things out is going a bit far. Try to be reasonable and see how she takes it. Then consider moving out or having her move out.