Zakat And Tax
Zakat is not only on savings, but also on your earnings (salary, business, etc.). The entire amount of zakat is obligatory upon you. You can deduct the taxes you pay from your total zakat. This video might provide some clarification: https://youtu.be/c2smJROWtY0
The obligatory zakat is the right of the state. You have to fulfill that obligation. If you owe more zakat than what the state takes from you, only then you can spend it in other good causes of your choice.