I'm trying to replace the mesh of a robe by creating a new body part and pointing it to the correct mesh (so it doesn't affect all generic robes with this mesh), then of course assigning the robe to use this new body part, but the game crashes upon equipping it.

What errors do you get, if any?

Making a clothing mesh replacer isn't as simple as that. Bahamut has a good tutorial on MMH and I suggest that you follow it.

No errors that I could see, just straight to the desktop.

I'll see if I can find that tutorial.

EDIT: Actually, can you send me a link? The search function on MMH is broken.

https://www.dropbox.com/s/mdtiatxjeeezo98/morrowind%20skinned%20armor%20tutorial.pdf

Does the body part have to have a specific name? The mesh I'm using isn't my own, it's from Uvirith's Legacy (Telvanni Servitor Robe), replacing the extravagant robe mesh used for MJP's Telvanni Clothes mod.