Explanation taken from catcahelpanimals.org)

The horses used in the bullfights are old and sold for few coins to the bullfighters. Their vocal cords are mutilated without anaesthetic so they cannot neigh in fear, especially after being stabbed by the bull’s horns. This is so that the audience is not aware that the animals are suffering. When the bullfight is going to start, the horse is mute, blindfolded with vaseline and cotton in their ears and nostrils; restricting their senses. The horse is covered by a peto (thin blanket) and ridden by the “picador” (the man with the “puya’). The whole puya gets inserted 3 to 4 times into the bull’s back and moved in circles, so the bulls get a few wounds 14cm deep and up to 45cm in diameter.

As the bull tries to defend itself, it strikes only to penetrate (with its horns) the horse’s neck or stomach. If the horse doesn’t die, it is taken into the plaza, where its insides are inserted back into its stomach with hay then sewn with rope or wire without any anaesthetic, painkillers or antibiotics.

The horse is then sent back into the bullring to be ridden again until it drops dead. If by the end of the day the horse is still alive, it is slaughtered by the butcher behind the bullring with the meat sold as dog food. Sometimes, up to 6 horses are killed by a single bull. The record number of horses killed by a single bull happened few decades ago. 11 horses laid slowly dying on the bloody arena.
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After the picador is finished with the “puya”, on comes the “banderillero” who carries the dreadful “banderillas”. These are stuck in the bull’s neck and back muscles to weaken. Each bull gets between four to six banderillas. With each movement the harpoon rips off the muscles with extreme pain.

After the banderillero comes the coward “matador”, who exhausts the bull with a red cape. When the bull gets too weak the matador gets the sword and attempts to stab the bull through its heart. But many times they fail and get the lungs instead, so the bull starts to vomit blood. When this happens, the matador gets a small knife (puntilla), and stabs the bull through it’s spinal cord (and continues until the bull falls).

But many times the bull doesn’t die after the 40 to 45 minutes of torture in the bullring; because the puntilla often doesn’t kill but just paralyses the bull. So later on when the bull is getting his skin ripped off by the butcher, he suddenly “awakens” and tries to run away.

In Spain alone, more than 30,000 bulls are killed this way every year.