They're indeed not mutually exclusive, in a matter of speaking. There are many ways cuts are needed and can be trimmed in the Defense budget, and they need to be done, yet at the same time not affecting or diminishing many of the capabilities we've worked hard to build and need to retain, lest we need them again and don't have them, as has happened time and again in our past.
When I talk areas of cutting, Im not necessarily talking specific forces like some of our Special Operations forces; I'd start with things like consolidating a military academy or two, or some of the social programs in the military itself.....things like Tops In Blue in the USAF, and other programs in both the DoD as well as specific services that if someone took a close look at, would see we likely don't need.
Insofar as "front line" items, one thing that needs to be revamped that wastes money is the entire acquisitions system for weapons systems, bloated and inefficient as it is, with its many outside influences and congressional nitpicking. Systems themselves that are fraught with cost overruns and/or don't operate to the standard they should. Etc, etc.
There are many ways that Defense needs to and can be cut; as well as many ways it can be improved, as well as many portions of it we need to insure we retain and continually improve upon. There's no one "talking point" answer, or even simple answers that can go into talking points, on either side of the table