My native language has a word for that process hence I am curious to find out if English has one. I searched for it on the Internet without success. Apart from "removing stem", I found "removing leaves" from cilantro.
In winemaking, destemming is the process of removing the stems from the grapes, and the same term is usable for coriander.
Verb (used with object), de·stemmed, de·stem·ming.
to remove the stem from (a fruit or vegetable); stem.
In food-prep, I've seen it mostly referred to as "stemming" which might appear counter to and the opposite action of "de-stemming". However, they are not.
- to remove the stem or stems from (a fruit, etc.) - Collins English Dictionary
Also, "stripping" as in "stripping the leaves off a branch of a tree"