Lossless cutting video (MPEG-4)
This is possible with the FFmpeg command ffmpeg -i input.mp4 -ss 0 -c copy -t 60 output.mp4. This would cut the video from the beginning -ss 0 to second 60 -t 60.

Be aware that -ss is and offset which -t is based upon. So -ss 10 and -t 60 would result in cutting to second 70 and removing the first 10. You can use the -to option to cut at a fixed time unrelated to -ss.

I'm not exactly sure how ffmpeg will handle GOPs but I think it will cut at the nearest GOP at the specified time.

Relevant question on SU: https://superuser.com/questions/138331/using-ffmpeg-to-cut-up-video