Defining “money the government needs” is key.
The government spends all the money it collects on the various programs it supports, including defense, foreign aid, social programs, national debt, consumer protection agencies, interstate hwy construction and maintenance, etc.
So, to cut taxes, scale back on programs (i.e., shrink government).
The Libertarian party, for example, is all about radically scaling back or eliminating practically every federal (state/local?) government-funded or operated program and thereby reduce taxes and government intrusion.
Libertarians contend that if citizens wish to have a service like social security, foreign aid or an FDA, they can organize and fund it themselves in the private sector rather than incorporate that activity under the “government” umbrella.
Disclaimer: I’m not Libertarian and don’t agree with some of their positions, but I think I understand them.