If a tenant's rent is past due, you can serve a 3-day "pay or quit" notice on the tenant. As you can infer, that instructs them to pay or move out. If they don't pay and don't move, you can start a legal action to evict the person.
Is it possible that over the course of your lease you have created a course of conduct that the tenant might use as a defense to eviction - that rent is due by the end of the month, as long as it's paid in full? It's plausible that a tenant might attempt such a defense; its chances of success, if raised, will depend on a lot more facts than are presently available to us.
If you simply want the tenant out, your best bet is to give your two months notice.

