The first example of catapulting plague victims into a besieged city was that of Caffa (Modern day Fiodosiya) in the Crimea. This was in fact the first account of plague in European history.
Caffa had been under siege by the Mongol (aka. Tartar or Golden Horde) army. The siege had been long a protracted. First starting in 1343, it was lifted by the arrival of Italian reinforcements in January 1344. The city was again under siege in 1345 however, a year later the Mongols started to die from a new disease - plague.
The Mongols tried to force the siege by catapulting victims corpses into the city and they were successful in spreading the disease to Caffa people. Even during the siege, Caffa's sea ports remained open and trade was conducted by Italian merchants with other nearby cities under Mongol control. Thus from here the plague was spread out to the rest of Europe.
Despite the use of plague as a weapon, it was the Mongols who capitulated to Italian demands and opened up to more trade. I think it likely that the Mongol besiegers were more badly affected by the plague than the Caffa inhabitants within.
Gabriele De' Mussi was a witness to these events. He wrote:
Among those who escaped from Caffa by boat were a few sailors who had
been infected with the poisonous disease. Some boats were bound for
Genoa, others went to Venice and to other Christian areas. When the
sailors reached these places and mixed with the people there, it was
as if they had brought evil spirits with them: every city, every
settlement, every place was poisoned by the contagious pestilence, and
their inhabitants, both men and women, died suddenly. And when one
person had contracted the illness, he poisoned his whole family even
as he fell and died, so that those preparing to bury his body were
seized by death in the same way.
There are only a few other examples of this. During the siege of Thun-l'Évêque in the Hundred Years' War, dead animals were thrown over the walls. However, there was no plague in the animals.
The siege of Karlstein Castle in Bohemia in 1422 saw the attackers throw dead human bodies over the wall, though again without plague infection.
It would seam that this form of attack is not as popular as some sensationalist historians make it out to be. Also the effects seem to be unpredictable. In order to have plague victims to throw over the wall, plague must be present in the besieging army. Not something you would want. Indeed disease is as much a problem for the besiegers as it is for the besieged. Sometimes a siege has been broken because the attacking army came down with cholera, dysentery or other.