How do I fix a HUGE increase in video file size

Have a normal mp4 1920X1080 movie video that is 2,376,943 in size. When I cut out some of the lead-in and ending credits of the video, which should make it smaller, and export, the size jumps to 3,885,049!! That’s over 1-1/2 times LARGER instead of smaller. What is the best way to get this thing smaller - Reduce the Frames/Second or reduce quality?

It will only make it smaller when all things are equal.
You need to tell us about your source file, the codecs used for the video and audio streams, the bitrate and compression used. Then you have to tell us which format and settings you exported to from Shotcut.

Change Export > Codec > GOP to something like 300 (or fps x 10), and set B frames to 3.

The current defaults are based on the YouTube preset because majority of users upload to it (good guess; I do not really know). And the YouTube preset is based on YouTube’s Recommendations naturally because people will complain otherwise.