Karna was one of the maharathis to assasinate abhimanyu along with drona, kripa, duryodhana etc. He has no mercy unlike shown in the popular shows. In reality, karna ruthlessly attacked abhimanyu and not give him death instantly.
It was karna who disarmed abhimanyu by cutting his bow & when abhimanyu picked the sword and shield to fight, he broke them as well.
Abhimanyu was the son of arjuna, the biggest opponent of karna so there is no chance karna had pity on abhimanyu in any way during the fight. The serials portrayed karna having a special relationship with abhimanyu because he is the son of arjuna (who is technically his brother). So, he give him a final blow by stabbing him with a sword and thus ultimately killing him which is a wrong depiction of the real incidents.
It was actually dushashana’s son who ultimately killed abhimanyu using the mace & karna witnessed abhimanyu’s death happily.