That statement is broad, and it's not clear what cuts are proposed. But the Defense Department and CIA, it seems pretty clear, wouldn't consider a study of climate change as waste.
In a report released late last year, the Defense Department said that climate change "poses immediate risks to U.S. national security." The 20-page report outlines a number of areas that require more assessment, including 20 specific, bulleted areas that the Department of Defense "must assess." In 2013, the head of U.S. forces in the Pacific stated that climate change "is probably the most likely thing that is going to happen ... that will cripple the security environment, probably more likely than the other scenarios we all often talk about," according to the Boston Globe.
In September 2009, the CIA opened a Center on Climate Change and National Security. Its goal: to study "the national security impact of phenomena such as desertification, rising sea levels, population shifts, and heightened competition for natural resources."
Climate change is a sharply political issue, of course, and the focus on it by Defense and the CIA both happened under President Obama. (Even in late 2009, however, retired Vice Adm. Lee Gunn of the American Security Project told NPR that that he believed "the vast majority of military leaders [are convinced] that climate change is a real threat and that the military plays an important role in confronting it.")
In his interview with Vice News released Monday, Obama noted the political opposition to addressing climate change.
"In some cases," he said, "you have elected officials who are shills for the oil companies or the fossil fuel industry, and there's a lot of money involved. Typically in Congress, the committees of jurisdiction, like the energy committees, are populated by folks from places that pump a lot of oil and pump a lot of gas." The link being that scientists believe the warming climate is linked to the buildup of heat-trapping gases in the atmosphere, which often come from burning fossil fuels.
Obama also noted another reason that his opponents object to addressing climate change: It adds cost over the short-term, and that can be politically unpopular.
For what it's worth, the House Republicans' document uses the word "environment" three times and the word "climate" twice. Two of the three uses of "environment" refer to the business environment; one of the mentions of "climate" does as well. The other use of "environment" can be seen in the excerpt above: It's a critique of the Environmental Protection Agency.