If you wish to exclude your EndNote citations from your word count, you can do this by creating a new style that hides all citations.
 
In EndNote select Tools>Output styles>New style:

To give the illusion of removing all of your in-text citation and bibliography references from your essay, so that you can obtain a word count without them, you need to create a blank EndNote Output style.

In the New Style window select File>Save as and give the blank style a name, e.g. "word count style" or "blank style":

Then save it in your EndNote styles folder in your H: drive, (if you do not have a Styles folder in your EndNote folder on your H: drive, we recommend you create one in order to keep all of your EndNote materials together). If the new style does not automatically save to your H: drive then you will need to find it in your documents/downloads and move to your styles folder in your H: drive.

You then need to find your newly created blank referencing style, and choose this newly created output style in EndNote, then also in Microsoft Word (see attached FAQ for how to find new styles).

As it is a blank style it will remove all citations so that you can then do your word count:

We have attached an example of this called 'Word_count_style.ens', which you can use, simply download and save to the EndNote Styles folder in your H drive.

Note: if you do not see your amended style in the list you may need to check that your style folder is set to locate your personal file space (H drive).

To do this: In your EndNote library Select Edit > Preferences > then in the grey box select Folder locations and your Style folder should be: H:\EndNote\Styles