Can a homeowners association have my verizon cable disconnected for late payment of association fees .

Does Verizon have a contract with you or with the HOA?

Some communities under a HOA will have a contract with a cable TV provider to provide access to the homeowners. If that is the case with your HOA then they very well may be able to do it.

What do the covenants and/or by-laws specify? Could you give a general location where this occurred? Is the HOA managed by your fellow owners or by a management company?
Has your late payment been made by now or still unpaid? If this is legal, it is a very cagey method of getting Assn. dues paid, but it could also be the "bright idea" of a new board member, who isn't familiar with the specific laws for your state or county or even city possibly. You need to expand with some details.