Is Josh Groban making up a word here (Spanish)?

maybe "deshojaste" from "deshojar" (it is pronounced 'desojar', because H is mute). It means literally "to pull off the petals of a flower" or "to pull off / to fall the leaves of a tree". Also, to tear or rip out the pages of a book or notebook.

It can be also "desollaste" (LL sounds like Y, similar to J in English). "desollar" means "to skin, to flay".

The Diccionario Larousse says "deshojar" means: "Quitar las hojas a una planta o los petalos a una flor" ('to pick off the leaves of a plant or the petals of a flower').

"Deshojaste" would be the second person preterit of this verb, so "me deshojaste la piel" would mean "you picked off my skin" (with your cruel goodbye).

Perhaps the reason you couldn't find the translation is that the word is spelled incorrectly in your quotation above (it should have an "h" in it).

Amazing

it is misspelled it is desollar ( desollaste ) and it means skinning as in taking the skin off that is why it says me desollaste la piel ( you skinned me, you took my skin off ) which is redundant is like saying you skinned my skin off but it is a song (poetic liberty) deshojar has to do with leaves it means to defoliate, to strip the leaves.

Desojar means to break or to burst.