Generally, self-defense and defense-of laws focus on imminent threats. Once the threat ceases, your legal options become limited. For livestock, it depends on the laws of the state. Some will allow you to pursue the dog a reasonable time or distance (or even indefinitely) even after the threat to your livestock is no longer over (this is probably based on the assumption that dogs are repeat offenders and it saves farmers the trouble of having to wait for them to cause trouble the next time).
If that woman wanted to kill that dog, she should have at least untied it afterwards or used a more discrete method. And if she told the police the dog was tied up at the time, well, she shouldn't have confessed.
The other issue that livestock defense cases turn on is whether the animal was attacking livestock. This is where some kind of surveillance camera system comes in handy. Such a system is also useful in figuring out native predator problems too.