There are two kinds of dogs who regularly attack.
1) Trained attack dogs like those used by the police or military.
These dogs undergo intensive training and must be extremely disciplined. The dog not only has to attack on command (they're generally trained to "hold" the person, getting one good grip and then hanging on) they also have to release immediately upon command. Think about how hard it is to train some dogs to drop a ball and you'll see the significance of this. Additionally, they will NOT attack unless expressly instructed to do so. (Dogs trained for ring fighting are taught different things, but they still have to be disciplined and responsive to their handlers. They would therefore probably fall under this first category).
2) Untrained dogs who are simply dangerous.
Dogs like this are unpredictable and their attacks are often fear-based. They may attack their owners and they will not stop attacking until they're good and ready (or until they're beaten off). The attack itself may also differ depending on the individual dog. They might get a grip and hang on, but they're equally likely to chomp down, release, and chop down again, over and over, causing damage to a larger surface area.
The first type takes great skill to train properly. The second type can easily be created by fools (and they usually are).
With that in mind, I have two questions for you.
1) Which type of "vicious" dog do your characters want to create? The disciplined police dog or the neglected, attack-anyone junkyard dog?
2) Which type will they end up with? They may want the first type but unless they've learned proper training tecniques, they'll probably end up with the second regardless. Certainly if their "training" consists of teasing and torture that's what they'll get. It also depends on the temperament of the dog. Some dogs respond to abuse by turning mean, but many others, I'd even say the majority, simply become cowed and fearful.