How do you remove splitted clip from original source

If you have trimmed a source file, a video, and you want to save the project so that that only contains the trimmed portion of the video you have to do the following:

Select the trimmed footage (movie layer) in the Timeline and select Pre-compose/moving all attributes to the new composition and trimming the new comp to the layer length and opening the comp. 

Then, with the new composition selected in the timeline, go to the Composition/Pre-render menu to render a visually lossless copy of the footage and replace the layer in the original composition with the newly rendered footage. If you have not fouled up the Render Cue's presets by editing them your project will now have a new footage source file that only includes the trimmed frames and you can delete the original footage file from the project.

Be aware that the new video file you rendered will be lossless and the file size may be much larger than expected, but you will no longer need the original untrimmed footage in the project. Unless you are an expert in video compression video standards, do not fiddle with the presets or customize the render settings.