What does ‘cutting with’ mean in ‘someone is right there cutting with the rest of them’?

I read the following lead copy in today's Washington Post article titled "Back home, GOP freshmen find fiscal responsibility can be tricky business."

What does "cutting with" mean? I don’t find the meaning of "cut with" other than in the ordinary usage of cut something with a knife, scissors or any other tools in a dictionary at hand, or in Google search. Does it mean alone, separate from the rest? I'm confused with the usage of basic and short words very often that are quite plain to native speakers.

As the government programs fell and the tens of billions in savings piled up during the budget debate in the House last week, freshman Republican Frank Guinta was right there cutting with the rest of them.

Henry's answer is exactly right. Here is confirmation:

A clearer, more complete use of "cutting" comes later in the same paragraph.

He wasn't willing to cut a subsidy for heating bills.

This illustrates that "cutting," as used in your example, had an object (parts of the proposed budget), and was not just used as an expression meaning something else.

The sentence in your question might be paraphrased in this way, for the sake of this explanation: "As the government programs fell and the tens of billions in savings piled up during the budget debate in the House last week, freshman Republican Frank Guinta joined fellow congressmen in reducing spending and removing parts of the proposed budget.

Here cutting means reducing government expenditure and removing parts of the proposed budget, while with means alongside and together.