It sounded to me as if the father lost control of himself when his daughter started verbally assaulting him. Must have said something so hurtful, that he couldn't take it anymore.
This does not justify his actions though. He might've used other forms of punishment, including withholding allowance, threatening to call the cops himself etc. His actions have done more harm to the child than good.
(His actions in this situation as well as in rearing his daughter to this point represent a failure as a parent.)
I would agree that corporal punishment in the form of slapping/spanking is acceptable only to a certain age, and definitely NOT acceptable for a man against his teenage daughter (step-daughter, adopted daughter and other relations where the girl is dependent on the man).
Having said the above, every situation is unique and general rules won't always work. In this case, the girl apparently has a history of breaking the law, and having seen the scratches on the man's face the deputy did the only thing he could do and had the girl arrested.
IMO, as a parent the father should now consider having the charges dropped in exchange for acceptance on the part of the daughter to undergo some kind of rehab/discipline program for kids and also do the extra community service that she'd refused earlier. If all goes well, that little episode will soon be behind them and they have a good laugh about how crazy it was later.
On a side note on corporal punishment for kids, it cannot be completely discarded since as we all know, people learn by example and for kids the learning is exponential in their early years. I think its a primal instinct to fear physical reprisal, and teaching kids that some things they do are just unacceptable by slapping them in order to draw attention to this is not a bad thing.
Would we really want children to get the idea that there are no consequences for their actions or learn the hard way by being punished publicly (such as being arrested, etc.) ?