How were heavily armored Cataphracts killed?

Disciplined infantry, whether armed with spears of swords or pikes, will almost always break the charge of heavy cavalry if they are well motivated and organised. The Romans came to know the devastating effect of properly timed charges from cataphracts and thus adapted their military greatly as a response to the lance armed cavalry fielded by both the Parthians and Sassanids. It is worth noting that the Persians relied on swarming missile fire in order to force the Romans into tight formations, whereby their cataphracts could charge successfully. The initial impetus of the charge would be devastating without doubt, but provided the Romans could loosen up and reorganize the Parthians would be forced to retreat (Those who didn't would be surrounded and killed.) Its also worth noting that most cataphracts had armor attaching the horse to the rider, meaning if the horse went down so to did the rider (game over) That being said, this combined arms use of cavalry was extremely effective against infantry, so the Romans had to come up with no ways to counter heavy cavalry.

Publius Ventidius Bassus is someone worth mentioning in this regard. In his campaign against the Parthians, Publius made sure his infantry was organised atop a slope or hill before battles. This would both negate the Cataphracts ability to outflank as well as severely reducing the charge impact. Any hors*m*n who tried to charge this formation was doomed. He also made sure his slingers were packed in close order behind his infantry (mainly as a response to horse archers) thirdly he made sure he had a sufficient force of light cavalry to harass the enemy cataphracts, as they were to slow to catch the unarmored roman cavalry. Publius's campaign was an embarrassment to the Parthians who had previously crushed the Romans at Carhae. In three separate battles he managed to trick the cataphracts into head-on charges against infantry, and the result was disaster for the cavalrymen. Another neat feature is that the Roman slingers were frighteningly effective against armored cavalry, more so than archers, as the blunt force was often enough to break bones through the cataphracts steel. Indeed the Parthian prince Pacorus took a led bullet from a sling to the helmet, and his skull was shattered (he died) Clearly Roman infantry, on its own terms could defeat Parthian cavalry, even being armed with swords. This was far from the only method, so I'll list a few historical scenarios quickly.

-At the battle of Nisibis, the Romans used caltrops to hamper the charge of cataphracts, where they then broke against the legions.

-At the Battle of Satala, the Romans stormed the Sassanid camp, Killing the hors*m*n in their sleep, and destroying the Royal Persian army.

• At the battle of Ctesiphon (363) Julian ordered his infantry to charge, dive under the lances of the cavalry, and slice open their stomachs, which was one of the only unarmored parts of the cataphract

• Emperor Carracalla managed to force the Parthian cataphracts to retreat from their own homeland after informing them that he had armed his infantry with pikes.

• Aurelian managed to trick the Palmyrene cataphracts into chasing his lighter cavalry. once the cataphracts were exhausted, the Roman cavalry turned and charges, using spiked maces to break the armor.

-Ventidius Bassus managed to surround Pacorus's cataphracts, but instead of closing in with his infantry, he unleashed volleys of led bullets from slings, which reduced the armoured regiments to nothing.

there are many more examples, which i obviously don't have time to go into detail. Countering cataphracts was a matter of combined arms effort. A mixture of light cavalry, light infantry, and heavy Infantry proved more than capable against armoured hors*m*n.

or you could do what the Byzantines did. fight fire with fire, get your own cataphracts.