Did the son of Sa'd bin abee Waqqas take part in killing al-Husayn? If yes, then why did he do so?

Umar ibn Sa‘d ibn Abee Waqqaas was the leader of the army sent to capture al-Husain (radiallaahu anhu), but it is not confirmed that he either commanded al-Husain’s killing or directly took part in it.

Although all of the reports about the incident appear to have some weakness, the most reliable narrations tell us that it was a person called Sinaan ibn Anas an-Nakha‘ee who actually stabbed al-Husain and killed him after Zur‘ah ibn Shareek at-Tameemee struck him. ‘Amr ibn Battaar at-Taghlubee and Zaid ibn Ruqaad al-Janbee are also reported to have taken part.[1]

And Allaah knows best.

Reference:

[1] Reported by Ibn Jareer at-Tabaree (At-Taareekh, 5/453) as cited in Mawaaqif-ul-Mu‘aaradah fee ‘Ahd Yazeed ibn Mu‘aawiyah (p.347) by Dr. M. ‘Abd-ul-Haadee ash-Shaibaanee