AVIDEMUX is free and should do what you want.

Install it.
Make a copy of the video to be on the safe side and open the cop with avidemux.

If you wan to delete from the beginning to certain point to keep the small clip area then click edit and select mark A.
If you wan to keep from the beginning and start deleting elsewhere move to where you want stop saving the video and click edit and select mark A.

Then move the slider to where you want to stop deleting and click edit and select mark B.

Now select edit and choose delete. You just eliminated everything between A and B.
Now change AVIMUXER to MP4MUXER in the pull down at the left side of the screen that says video output.

Now click file at the top and choose save and enter the name for the new movie.

Thats it. After you pick the name it will make the new movie for you.