Use the “R” key to draw a yellow range box in the timeline for the part you want to export. Then do File>Share, etc. and it will only export the portion highlighted by the range box. You can then do that on other portions.
It is not necessary to cut the timeline or delete part of it for this. See https://support.apple.com/kb/PH26141?locale=en_US
You can also use a similar export method to export multiple ranges or clips from the Event Browser as a single batch. Each will be given a unique name. See https://larryjordan.com/articles/final-cut-pro-x-10-4-4-batch-export/
In FCPX the optimal workflow is spend lots of time in the Event Browser marking favorites, rejects and keywords. Then use the various filters to hide rejects, show favorites, show keyword collections, etc. For multicam or material with external audio that should all be synced in the Event Browser, not on the timeline.
Only after careful organization and curation of the material do you move to the timeline stage of editing.