There are a couple of methods one could use to accomplish this.
The mainstay is the puppy fountain.
Essentially, you create a shaft that rises up 9z or so directly above the meeting hall, which leads to a tiny room with an open pit which is the "top" of said shaft. It has 1 tile of floor adjacent to the hole, and is completely walled in. On that tile, you place a male and a female dog.
Overcrowding, and pupsplosions take care of the rest. As the puppies are born, they can't leave the 1x1 tile of floor, and overcrowding starts, leading to puppies and dogs attacking each other, and eventually, random dodges, which makes them fall down the pit. With a fall of that great a distance, they explode into gore when they hit the floor. Make sure dwarves can't stand on the big red X, but can still witness the relentless attrocity.
Another method bears the risks of making a dwarf insane, but is targeted.
Train lots and lots of hunting dogs, and assign them to the target dwarf. Carefully observe the happiness of this dwarf, and whenever he/she becomes exctatic, kill one of the dogs assigned to him. This is the same as suffering a tradgic loss, but without the network of friends to contend with. Leaving the pets to rot further enhances the insanity inducing effect.... so be careful to only massacre one doggy at a time, and only after Urist McHeartless returns to being exctatic. When he reaches the "doesn't care about anything anymore" trait, he should become locked in at "fine", and be immune.
The first is passive, and treats the whole fortress, while the latter is active, and works on targeted dwarves.