You can just select A(start) and B(end) of the section you want to cut out and press del it will delete the selected area only,then save the file.AVIdemux http://avidemux.sourceforge.net/
I've used the program for years to do what you describe.
drop your file in
set end marker at beginning of section you want cut and save file as 'A'
go back and set beginning marker at end of section you want cut and save file as 'B'
close current project ctrl+w
drag file 'A' in, drag file 'B' in and save final file.