I'm studying to be a Psychologist, and I can't discern too much about the situation without proper information on a suspect/perp. BUT I can say that for someone to do this, they would have to have either developed a sinister hatred of puppies somehow, have not recieved the proper socialization/upbringing to control themselves, and/or there is a symbolism here.
I can see two likely scenarios here.
Symbolic Displacement of Revenge -
The dogs were killed/maimed through detonation of explosives within their mouths. This suggests a likelyhood that the perpetrator(s) had experienced a significant trauma involving a dog I.E. being attacked, mauled, chased down, etc. The dog may have disfigured or greivously injured this person primarily through biting, chewing, the damage being mainly inflicted by the dog's mouth. Now, this would relate to the killings/maimings of these animals in that perhaps the dog which did the attacking had recently sired this litter of puppies. This act of revenge was centered on the puppies and their mother, as the dog which did the attacking would have been put down, removing the chance for direct revenge on the part of the attacked, so they went for the next best thing, it's "wife and kids". And what better way to get back at a dog which mauled you than to attack the mouths of those "wife and kids"? The explosives merely offered a more effective and brutal revenge, which was justified in the eyes of the perp.
The other scenario is that these were just a group of kids who for a whole slew of reasons have developed into pitiless, merciless, sadists (which bar no argument is the fault of the parents and to a lesser degree, other such adult figures, like it or not), and this was just another act of amusement for them, at the expense of a dog and her pups.
Whichever may be the case, the simple fact is that these people simply cannot be trusted to function safely within our society, and IMO, should be taken out into the middle of the Arctic Sea and tossed overboard. If they turn up alive somewhere, then we re-enact a certain ending scene of Wanted: Dead or Alive starring Rutger Hauer as the guy who pulls the pin. If you've seen it, you know what I mean. If not, go watch it, it's a good movie.