Rocketman,
If you can port the object out of mesh mixer to an OBJ file, you should be able to get it into Blender and delete the extraneous pieces that the mesh created by highlighting the errant pieces and hitting the delete key.

I've seen the mesh.  Imagine a classic Beethoven bust that is curved inward from the front base to the top of the shoulders in the back.  The overhang is ridiculous, so he wants to extend the base back to remove the overhang.

Not a bad solution, and it should be possible in most mesh editing software, provided you can get it to import correctly.

ah, that sounds rather trivial, if, as you said, you can get it imported properly, and more importantly, in a format that can be mesh edited, or at least acted on by Boolean modifiers. to add a new mesh if necessary.

Not a bad solution, and it should be possible in most mesh editing software, provided you can get it to import correctly.

Any suggestions? I can't find a software that allows me to basically slop on a bunch of extra material on the back of my model.

is the face you have a flat/hollow mesh, and you want to extend the head to look realistic? or what.. i think we're gonna need to see some pictures. i think i understand what you mean and i know of a few head modeling tutorials that you can watch starting from after the face is modeled, to show you how to add the rest of the head. but not being sure what your working with im not sure if they would help you or further confuse.

and when you say "design", do you mean engineering design principles, or just using the software? what kind of modeling do you want to do? mechanical parts for robots/machines, or sculptures of figures? answering these questions will give you some idea of what software to learn. gonna pitch blender again here, since its more than capable of both. but there are other softwares that are more suited to artistic modeling IMO. so let us know what your actually trying to learn and we can maybe point you in the right direction.

Can you post a parasolid or dxf?

I don't know what those are. Actually I think I found a method that works with meshmixer. It's a bit dodgy, but when I take the time with it I can avoid doing what needs to be done without destroying the opposite side of the model. lol.

Having said that, fool, have you looked for Dummies books? (That last part there, that was stupid humor). I bought the Dummies for Sketch Up althoughi t was a little light on substance, I thought. I may be a dummy but hey...

I see stuff all the time on Thingiverse and elsewhere that I wouldn't know how to begin to make.  I want tutorials on the principles of their construction, not just what buttons to click to make it happen in Sketchup.

go to a community college and get into graphic design and 3d modeling

I can't afford to go back to college, and due to too many credit already couldn't even get a loan. Computer classes are unlike math or philosophy classes in that you absolutely need to pay to take them since you'd need to use their equiptment while other classes someone can just sit in on. I am looking for online resources.