Is it possible for a diy'er to successfully and safely remove black mold ?

It's tempting to try this yourself but unless you have the right gizmo that tests for mold, you're just going to be wasting your time as the black mold will come back.

Just how big an area is this and just how long has the mold been there "brewing"?

I have to agree with the "how extensive is the damage"? Once that's answered, then "How long" comes into play.

Remember mold starts to grow within 24 hours. Preventing it within that time is critical. It loves drywall.

Positive pressure, HEPA filtration, respirators, disinfectants and ozone generators are used by professionals.

While doing the removal, you have to not spread the mold spores.

So can you safely cut the material out and bag it without spreading the spores?

Also if a professional does this removal the job comes (usually) with a guarantee that the mold will not return. In an instance when I worked at a modular home dealership a home was set on a basement and then the basement floor was not poured yet. The home had black mold underneath in the full basement and onto the underside of the home. This home had not been lived in as yet at this point. It had rained considerably and was not properly drained out in the basement area. The professional mold remover company had to end up removing the carpeting and carpet padding as the mold had intruded into the pad and carpeting from below. That will give you an idea of just how intrusive the black mold can be! The modular home was vacant for about 2 months during the spring rains.

After the professional crew finished treating the home's underside the home did not get any black mold back. And the home had a 10 year guarantee for the mold not to return. Don't know exactly what kind of chemical was used to dissipate the mold and effectively kill it, but I do know that this mold removal process for a home of 1,400 sq ft was in the $5K area when they where done.