Is it permissible to mix the money of Zakaah and Sadaqah and then give to the poor people?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad  is His slave and Messenger.

There is no harm for paying Zakat together with optional charity; however, one should make the intention about the money that is prepared for Zakat when giving out the money. That is because having intention is a condition in acts of worship, as one distinguishes by intention between one act of worship and another. The Prophet said: "Indeed actions are judged according to their intentions. So every one will be rewarded for what he intended." [Al-Bukhari and Muslim]

Ibn Muflih from the Hanbali School said: 'Intention is a condition when giving out Zakat.'

Allah Knows best.