As the title reads.

I need a corpse. But I don't want the mutilated torso, though for now I am using it. I also understand the GECK does list dead wastelanders and such but what I am looking for in particular is a headless corpse.

Is there a way to remove the head from a person through the GECK?

I need it for part of my mod.

I used killactor to set up murder victims how I wanted them. May work for your purposes as well.

Here is the wiki link: http://geck.gamesas.com/index.php/KillActor

I'm going to try that. However, does the person in question need to be alive when the PC walks in and then dies? Basically, what I have going on is there is a room in my mod where a "doctor" was killing ghouls to make certain items. So, the ghoul on the table would already be dead prior to the pc walking in.

It depends of what you want exactly. You could create your creature already dead (just give it 0 health), place it as you wish on the operating table in the GECK with F4 CTRL-Alt and add a script to dismember it on load. Tweak the one already in the GECK to make yours just to remove the head
I never tried with creatures, but with characters it works.

Yeah, basically I just need a body of a ghoul with no head. I don't even want the head in the cell because I am using a skull for the head. I'll see if that works for me.