All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If you mean that the two congregations are held at the same time and in the same mosque, then this is not permissible for many reasons:
1- This is contrary to the practice of Muslims since the time of 'Umar until today, that it is only one congregation which is held for Taraaweeh prayers at the same time, without holding a second congregation. It is reported that 'Umar gathered the people to perform Taraweeh prayers: the men led by Ubay Ibn Ka'b and the women led by Sulaymaan Ibn Abu Hathma. Moreover, 'Arfajah Ath-Thaqafi narrated that 'Ali ordered the people to perform Taraaweeh prayers: he appointed an Imaam to lead men and another to lead women, and I was the Imaam appointed to lead the women. [Al-Bayhaqi]. To conclude, there were not two congregations for men at the same time, but only one congregation. This was the practice of Muslims since then, and never one acted differently. Therefore, making two congregations at the same time and in the same mosque is contradictory to this confirmed and deep-rooted Sunnah.
2- Making two congregations at the same time is contradictory to the purpose for which the congregation is legislated, which is to unite the Muslims and bring them together united as one hand. Additionally, it is a sign of division among the praying people.
3- This may also lead the people to make more than one congregation for the obligatory prayers at the same time with the pretext that the youth want to extend their prayer and the old to make it short.
Therefore, we believe that it is not permissible to establish two congregations at the same time in one mosque. The people in charge of the mosque should prevent this, and they may fulfil the need of everyone –between those who want the Imaam to extend the prayer for a long time and those who want to make it short- by leading a medium prayer, not too long and not too short.
Allaah Knows best.