In principle, one could probably do this to a rooted phone by removing all the Google apps, and all the Google services, and giving up the other apps and services that depend on them. It would be a nontrivial task, and the steps would likely be different for each phone model (and possibly each OS version). I don’t know of a project that does this successfully. You might try searching xdaforums.com for someone who has done it.
However, I wouldn’t depend on Google services staying disabled when Google still controls the OS.
IMHO, it’s safer and easier to replace the entire OS.