Right now, my hair is a little longer than shoulder length and brown. I want to cut it really short, then dye it black. Would the black dye harm my freshly cut hair or scalp? Mind you, I don't mean short as in a bob, I mean short as in, I'm-going-to-spike-it-up-with-hairgel short.

I would dye first, cut after. If you color too soon after cutting, the ends are too porous and absorb too much colour.

Tick

I'm not sure why you think that black dye would harm the freshly-cut hair. The ends, being freshly cut, would not be porous (that occurs with time and other chemical treatments, or air oxidation). As for the scalp, that would be the same regardless of whether you've just cut the hair or not.