If the US government stopped collecting taxes, that would heavily devalue the dollar. The dollar is the official currency of several other countries so it wouldn't go to zero, unless they too stopped collecting taxes. Of course, even if that happened, there would be some value, because by US law, the dollar is legal tender, which means offering a third party a US dollar should be sufficient to settle any debts. Of course, as the dollar is also no longer useful to any third party, more and more dollars would be demanded as the value slowly fell to zero.

But yes, if the US stopped collecting taxes, the dollar would heavily devalue, and eventually reach zero

In general, the value of fiat currency comes from how useful it is in satiating the demands of the government backing it. Usually, that is taxes, but there are a few other ways fiat is used that have to be taken into account (judgements, etc)