Can a homeowners association force a homeowner to evict a tenant?

Perhaps. If the tenant does not abide by the governing documents -- living in the community like an owner -- then the association may require that the owner evict a tenant. The governing documents may state what behaviour is expected from tenants.

This action may be the last in a long list of attempts made by the association to bring the tenant's behaviour into compliance with the governing documents.

An owner who resists removing a disruptive tenant adversely affects the value of all the property involved in the association's real estate asset base.

A board that uses this tactic to remove a tenant based on prejudice or other illegal basis could be in violation of local and Federal Laws.