You need to cut away three distinct parts of the crab, the gills, the apron and the head section.
The gills (where the knife in my hand is working on above) are right under each side of the pointed end of the top shell. If you look closely you'll see that the top shell is flipped over or back as I cut. You don't want to pull the top shell off completely. On a soft shell crab the top shell is held on only by the center section of the crab. You'll see what I mean when you pull the top shell over.
Next is the apron... if you look at the top right of the photo above you'll see a crab turned upside down. There is a knife whose blade sits at the base of the apron. The apron is pulled back from the crab. That part needs to come off using a scissors.
Next is cutting out the head section (eyes and
mouth). What you see to the right are kitchen shears, and, they are positioned at an angle to cut at a short angle. Take the shears and cut a small wedge of sorts to remove the eye and mouth section.
Now you ask: what about the intestines? They remain intact and are cooked fully, so, they won't hurt you or taste bad. If this just completely grosses you out you can do the following. When you go to eat the crab, break it in half and remove the intestines. The only other way to remove them before cooking is to partially remove the top shell, or, cut the crab in half and remove the intestines. It's your choice.
Want to learn more about the soft shell crab? It's right here...