www.alphadictionary.com

A recent post about phrases like ‘my homework needs done’
makes me wonder if there’s a word, analogous to ‘elision’,
for excision of a word or words. Why not a Board Index category for ‘Vocabulary’? Not etymology, but usage of the familiar, and discovery of the un-.

No idea why I didn't say this when I first thought it, but...; wouldn't this fall nicely under the Grammar section? Words and how to use them, or not use them.

Well, the main point was not the usage, but looking for a word for it.

A recent post about phrases like ‘my homework needs done’
makes me wonder if there’s a word, analogous to ‘elision’,
for excision of a word or words.

Ellipsis?

In the following link, this construction is referred to as "need + V-en":

https://ygdp.yale.edu/phenomena/needs-washed

Thanks much for the article.
And I do believe ‘ellipsis’ serves perfectly. Apparently, I was mistaken, always associating the word the the familiar three or four dots.