Is there a word for "butchering" a chicken into parts but if the chicken's already dead?

In the UK at least you can "joint" a chicken. British TV chef and cookery book writer Delia Smith gives full instructions here but other online sources also use the term. Whether it's used in the US I don't know but as John Lawler suggests "cut up" in his comment I suspect not.

You can also spatchcock or butterfly a chicken but this merely removes some of the bones and lays the bird flat for faster cooking, it doesn't cut it into pieces.

Butchering an animal does not imply that it is alive. You can butcher a dead animal. In fact that is a normal use of "butcher", being what a butcher (noun) does.

A verb for cutting up a chicken is to fabricate. My son is in culinary arts and this is what I just learned today from him. I googled "fabricate a chicken" & "chicken fabrication". Never knew it had anything to do with cutting up chicken. HOW TO: FABRICATE CHICKEN