If you would like to evict the tenant you should serve her with a notice. An eviction action based on non payment usually requires a 5 day notice. Once your tenant is served with the notice and still does not pay the rent due, then you can file an eviction action against the tenant at the court. Once a court date is set, then the judge will order the tenant to move out if he or she believes that you have a valid claim. You should understand that it is quite long and possibly frustrating procedure.
In addition, DO NOT ever cut the utility off from the apartment since it is illegal for a landlord to do so.