Blender doesn’t know you want to cut edges in half, it just knows you want to remove vertices. You need to put some vertices down the midline of the head first. Try the loop-cut tool:
In Edit mode, position the pointer on the uppermost visible edge.
Do Ctrl-R. This will put a purple line down the vertical center of your box. Press Enter twice to create vertices along this line.
Now remove the left-hand vertices as before.
Then check out this page on the basic elements of CG modeling:
You have subsurf on. Thats the problem. This is a common thing amoung new blender people. Basically Subdivision Surfaces is a MATHMATICAL calculation on a mesh object to give it s smother and more organic appearance during rendering and in a 3D window. [One of the blender experts here correct that statement if its wrong. I hate to steer newbies in the wrong directions. It is not the TRUE MESH which is made of discrete points in memory.
In order to delete have the face you can do one of two things.
Turn subsurf off temorarily and then delete the half. When you get this you will get your “rougher” real mesh back. Then delete the half you want. Then turn subsurf back on to see how it will look “smoothed”
You can turn the subsurfed mesh into REAL mesh but press ALT-C[Check that hotkey. Its been a long time since I did anything with subsurf]
This will make blender convert the mathmatical representation of the subdivision surface into actual vertices,edges and faces. Two warnings though.
A. This is a ONE WAY conversion. Once a subsuf is converted to a mesh it cannot be converted back to a subsurf to get the same form. You can apply subsurf on the new mesh but that will apply the math to THAT mesh not your original one.
B. You will create a mesh that has tens,hundreds or even thousands more vertices and faces. So if rendering or HD memory is of concern remember that you just made a much “heavier” mesh object.
im new to blender, but i have a suggestion that worked in cutting a sphere in half if you want to try it.
-Select half of the vertices in the object. Use ALT to select multiple vertices in the same plane. Use Shift to keep adding to the vertices selected.
-Press X. Delete FACES.
-Press A KEY
-Press SHIFT + D
-Press S KEY.
-Press 1
-Press - (MINUS)
-Press Return.
Object is now halved. Probaby not the best way of doing this but i believe it ought to work. If You intend to line these pieces back up it could be tricky if you move them out of line with eachother. So i suggest you only move/rotate them along thier local axis. Let me know if this works for you.
EDIT- Also this will clealy only work if you want to cut the object exactly in half and keep both halves. If you only want one half it should work fine just deleting the faces.
my way just assumed he wanted to keep both halves thats all. Buy yes you’re way works much easier and it is still possible to make a dupe. But then i never said my way was the easiest or best, i just said it would work.