Taxes don't remove money from the system (whichever system you refer to).
They don'y magically exit anywhere. They are used to invest in new things, fund government salaries, public services etc. etc. Taxes stay in circulation.
Taxes are an expenditure to the taxpayers but income to the state.
However, as the state utilizes the income, it's paid back to the taxpayers either in services, goods or even direct salary if you happen to be employed by the state in one way or another.
Example: Rolf Roadmaker pays a tax. Then he's hired to build or fix some road, which is funded by the state.
Could you exemplify what you mean by "taxes remove money from the system"?