It would be unusual for an HOA to have access to the utilities' controls to turn the utilities off. Water, cable, and electricity are usually provided by other companies.
Water and electric companies have to go through procedures to turn off those utilities. A person would get several notices from water and electric companies before someone one comes to the building to turn the meters off. If you are within the City of Seattle, the City likely is the company that provides both water and electric services.
Cable companies are also regulated. However, since cable is usually not a life or death utility, the cable companies can turn off the service any time.
If the utilities are provided by other companies, the HOA would be foolish to even touch the controls of those companies.
Even if the HOA can physically turn off the utilities, the HOA likely will need to follow the procedures governing the HOA.
The answer to your question depends on whether you live at an actual homeowners' association (formed under RCW 64.38) or in a condominium association that was created before July 1, 1990.
Only condo associations created under the Horizontal Property Regimes Act (RCW 64.32) which ALSO have an explicit grant to terminate utilities in their Declaration have the authority to terminate utilities for non-payment of dues.
So if you live in an HOA or a newer condo, utility termination is not an option for your association.
We strongly encourage homeowners who are behind on their dues to communicate regularly and openly with your board of directors. Resist the temptation to ignore this problem until times are better financially; by then, your association might have taken legal steps to collect (including a lawsuit to foreclose the association's lien against your property) which could add thousands to the amount you owe.
This answer is intended to provide general information and not legal advice, and does not create an attorney-client relationship.