GURPS is all about modularity and customisation, so it depends on how much detail you want. Fortunately Dungeon Fantasy RPG (a standalone RPG “powered by GURPS”) puts monster-parts in the spotlight as a possible loot, so there's a set of skills already assembled for this kind of detail.
Single skill option
If you want a single-skill way to model this, the one that comes to mind is Surgery. It comes with a seal of approval from the line editor, who made it the “getting monster parts out of a monster without damaging the parts” skill in the Dungeon Fantasy RPG and the supplements that preceded it. This is what I'd go with if internal bits are valuable for “infusing” during weapon and armour crafting.
(Normally Surgery is species-specific, but if you're going for a single-skill monster parts treatment, ignore that and just let it work however. Instead now, it's the skill at cutting into things without messing up the valuable parts.)
If you're thinking less internal organs and more easily-harvestable things (skins, horns, etc.), consider instead Survival as the one-skill way to harvest monster parts, since that knowledge is naturally part of a hunting and foraging skill. This is what I'd go with if I was using monsters parts as the main materials for weapon and armour crafting.
Multiple skills option
If you want more detail, or you want to see some diversity or specialisation among your PCs, DFRPG's monster-parts rules provide some more skills for monster parts harvesting:
- Use both Surgery and Survival, for internal and external parts, respectively.
- Poisons for milking venomous creatures/monsters — for obvious reasons.
- Hazardous Materials for collecting and safely containing weird non-poison substances, like flesh-eating slime or acid blood.
Knowledge skills before harvesting option
DFRPG further suggests skills for identifying valuable parts, before being able to harvest them.
Again, this is another layer of detail that you may or may not want. It can also be combined with either the single-skill option (just pick one knowledge skill), or with the multiple-skills option.
So if you want monster parts to just be obvious when seen, or be well-known already among the PC population, you probably don't want this level of detail. If you want to make monster parts harvesting its own challenge to both player skill and character skill though, you might consider these DFRPG options:
- Naturalist to identify external parts removable with Survival, like the aforementioned skins and horns.
Physiology ([creature-type]) to know/identify what's inside it enough to even think of using Surgery to get internal organs.
Notably, DFRPG uses the fact that this is specialised to a creature-type category (though still pretty broad ones, like “undead” or “demons”) as a way to gate the Surgery skill by creature type, without requiring PCs to invest in many specialisations of both skills.
- Thaumatology to identify weird, magical monster parts (like, what parts of a lich are actually even useful?), before a Surgery roll to get it out intact.