The first link below is to a State website that provides a wealth of information about landlord-tenant law.
You can go to small-claims court (see second link below) to recover unpaid rent and utilities and damage in excess of the amount of the security deposit.
Since the tenant is responsible for paying the water bill, shut-off due to non-payment is the tenant's problem, not yours.
Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.
If this tenant is leaving in a month, then you don't have enough time to evict them, and it's not worth your effort. But maybe if their water gets shut off, they'll leave early and mitigate their refusal to pay the last month's rent.
You can't shut off their water and "constructively evict" them, but you can let the water company do it, and not pay their bill for them, as that's their responsibility.
The tenant's security deposit will go toward their unpaid rent, anything you have to pay for the water so you can re-rent the unit with water, and any damages done to your unit. If this amount exceeds the security deposit, you can sue them in Small Claims court.
Linked below is a landlord's guide written for non-lawyers that you may find useful.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.