Adobe Premier Elements 2018 - How to create trimmed/cut video without exporting/re-encoding

One partial solution is to select your video and then use FX-> Effects - > Keying -> Four-Point Garbage Matte and change the view area to the shape you want. The unused area will be black and have the same effect as trimmed. If by "cutting" you mean, cut the video, just click the scissors on the scrub bar where you want to cut. A double snip will give you a section you can ctrl-X delete.

Premiere Elements does not do that, nor do most other NLEs.  (Non Linnear Editors).  What you want is sometimes called "Smart Rendering".  Try a Google search for "smart rendering video editor".  One that will come up is:  Best MPEG Video Editor Software | TMPGEnc MPEG Smart Renderer 4 .  I've never tried it but some that have like it. 

Good luck finding what you want!