Technically, you can't cut a clip from one project to another.
But you can:
* Output a segment of your project using Publish & Share and then use Add Media to add it to another project; or
* If the clip is just a clip on your hard drive, you can just use Add Media to bring it into your second project. You can use the same clip in as many projects as you'd like.
You can do a copy/paste insert between two Premiere Elements projects, using Premiere Elements in conjunction with the ClipMate (a Windows only 3rd party program).
With version 12 and ClipMate, only transitions do not go along with the other copy/paste insert data as explained in the blog post.
If you use the export from project 1 and import the project 1 export into project 2, be sure to consider the project 1 export settings so that export properties will be consistent with project 2.
Please let us know if either of the above works for you.