I gave it a whirl. There are some built-in constraints. For instance, you can't take away minuteman missiles. Nor can you cancel dental insurance for servicemembers.
Also, you are not allowed to entirely disband any component. There must be at least one aircraft carrier, one army brigade, etc. Force reductions in general staff are limited to 50%.
But I tried. I took away everything I could. Cranked every slider to its minimum value.
For a total reduction in personnel of 1,071,000.
For a grand total annual savings of...$184 billion.
That savings is roughly 30% of the actual us military budget (depending on what year you compare with)
In other words, if the US military shrinks to its absolute minimum level, it somehow still costs 2/3 of the money. According to the CBO's online slider tool, at least.