No, it’s incorrect. Taxes and zakat should be paid differently.
Pay attention that tax and zakat have different concepts and are used in different aspects so they should be paid differently. Some of their important differences are:

1. Paying zakat is an Islamic order but tax is a government order.

2. Tax is spent for government needs but zakat is spent for Muslim needs.

3. Zakat is used to remove poverty but tax is used to supply expenditure of government.

4. Zakat has specified limitation and is belonged to specified materials but tax doesn't have specified limitation and government experts specify its limit.

Etc...

(Reference in Persian: Al-Jami li-Ahkam, volume2, page732)