The most common and most likely answer to this crossword clue is the 9 letter word EXCRETORY
I've seen this crossword clue in The Guardian
E
X
C
R
E
T
O
R
Y
Buddy explains!

The straight part
We know that "eliminating waste" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case eliminating waste = excretory.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EXCRETORY mean?
EXCRETORY noun- A duct that helps to receive and excrete matter.
- Of, or relating to excretion.