There is no criteria set in place that would determine whether a department or administrative arm of the Executive Branch is indeed "unnecessary." That list of criteria is painfully absent. Instead, the order offers a 180 day window for the public to voice their concerns, with again no insight on whether these concerns will influence or help determine the outcome of these cuts.
What's more troubling is this section:
Anything can be determined to be handled by local governments and city localities. The state of New York, for example, already has a Dept of Education, an Energy Department, even an Attorney General and National guard. It could be argued that most of the executive branch is redundant if we were to ignore the nuances of what they provide, and the fact that state localities on their own are cannot sufficiently provide for their residents w/o federal aid in some measure. Moreover, these departments in the federal government act as an oversight, compelling local governments to comply with federal laws and regulations that protect citizens against the possible malfeasance of local government. In other words, if we got rid of the EPA, before the Flint Water Crisis broke - would things turn out the same? No. Now think about the other parts of the Executive Branch that could be labeled "unnecessary" to some, and vital to others.
You can find the full Executive Order here: