How can my mom evict me, if I pay her rent?

If there is no written lease give you 30 day notice to move out ( assuming you are not a minor child)

If mom is the property owner or leaseholder, she can con control who lives on the premises. If you have no lease then she can evict you as long as she does so legally.

Same way she would evict any other tenant. Assuming you are an adult and have no lease with her or that you have a lease that you have violated she can get a lawyer and get a court date and have you out. Just becaue you pay something doesn't always mean much.