Copying the split segment of the clip to a new project, and then exporting out from that project, would be the only way to preserve any edits (i.e, your split) that you have made. In the old iMovie 6 one could select a segment in the timeline and share it out separately from the rest of the clips in the project. Unfortunately that helpful feature was eliminated in later versions of iMovie.
As a matter of work flow, you wouldn't need to delete the new project and create a new one each time. You can export a project as many times as you want. So, put segment #1 into the new project, export it out, and then delete segment #1 from the new project and import Segment #2 and export segment #2 out. Repeat the process with segments #3, #4, etc. until all of your segments in the master project have been separately saved. Once they are saved you can keep them in a finder folder for later use (recommended) and/or import the clip segments into a newly created iMovie event for access by all of your projects. Keeping them stored in the Finder and in iMovie as well, would double the drive space being used. However, if you are going to store the clips in one place, in my view it would be better to store them in a finder folder where they can be readily accessed for different purposes and not be trapped in an application that might get corrupted or become obsolete. If the one place that you store your clips is in the iMovie app, be aware that iMovie libraies sometimes do get corrupted. Also, it can be awkward to retrieve clips for use outside of iMovie.
-- Rich