So when I cut a video I recorded in have and save it as a .veg I would like it so the original full video i recorded could be deleted but I would still have the .veg file that i cut in half that i could further edit later n if i wanted.
No a .veg file is not a video file.
A Vegas project needs a video file AND a .veg file, get it?
As musicvid stated, YOU NEED TO KEEP THE SOURCE MATERIAL until you are through with a project (at least). A VEG file is simply a series of commands and the added material such as titles. It does not contain any source material.
an I export it as a different file for the purpose I'm looking for?
Yes, you can render the project to a new video file, normally try to choose a lossless codec if you are planning on more editing at a later date. But remember you can't remove any titles that are rendered in the file or change any effects. You need the original source and veg for those types of changes.