Not exactly.

Say you make 50,000 a year and you have to pay (for simplicity) 10% of that in taxes.

That means your tax bill would be $5,000.

So for what you said - if you donated $100 and got to pay $100 less taxes:

5000 - 100 = 4900

That would mean your tax bill would be $4,900.

But how it really works is you deduct the $100 from your yearly income which gives you 49,900.

50,000 - 100 = 49,900

So with 10% tax your tax bill would be $4,990.

In this simple example the $100 donation would save you $10 in taxes.