Saga can only pick up strays, which is a duty the town board may allocate. Criminal law, requires police enforcement. Not only that but as Saga only receives voluntary donations and barely scrapes by, it is helpful for the public to place the responsibility with the authority that is funded to provide the required service. As stated, Saga can talk to them, but any enforcement would require the involvement of the police.
And yes, hurting the dog may only escalate the situation both with the dog and the owner.