When a government spends more money than it collects, that is called a "budget deficit" or just a "deficit".
The phrase "cut the deficit" means to reduce the difference. For example, if the government was spending $100 billion per year more than it was collecting, and now it's only spending $50 billion more per year, then a politician might say:
We've cut the deficit in half.
We've cut the deficit by 50 percent.