The reason you can't cut your face in half is because blend shapes depend on point order. In the simplest terms, every point is assigned a number, and your blend shapes deform on a component level. This is why when you duplicate a base object, translate it to the side, and assign a blend shape, your base head will not also move to the side when you dial up your slider. Because object transform information is not a deciding element in how your blend shapes calculate (this includes negative scaling to get mirror copys). However, if you went into component mode, and moved the verts/CVs instead, when you dialed up your slider your base WOULD move to the side. Your blend targets need to have matching vertex order corrosponding to your base shape, because when you dial up your slider, maya thinks " now component number 3 is relocated to this spot, I'll move #3 on the base to match #3 in the target. When you are cutting apart your targets, you are changing the point orders to accomodate the new geometry that has been combined or added. this is why you get spaghetti. #3 used to be in the lip, now its on the eyebrow.
the only way that I know of to get symmetrical blend shapes without modeling both sides is if you are using polys. There is a mirror script on this site in the mel section.
good luck!