Here are the examples from the documentation in 18:32:
Rule for supplying a missing noun while listening (this is the ambient sound rule):
now the noun is the location.
Rule for supplying a missing second noun while unlocking:
if the skeleton key is carried, now the second noun is the skeleton key;
otherwise say "You will have to specify what to unlock [the noun] with."
What you may be running into is that you’re only supplying a message and not an instruction for the “Rule for supplying…” rulebook.
Note that, in order for our activity to succeed, we do need to supply a grammar line allowing the player to try “unlocking it with” using only one noun. Otherwise, the command “unlock something” will still produce the question “What do you want to unlock the door with?”
You could probably use the “mistake” rules to just disallow the action CUT without a noun:
Understand "cut" as a mistake ("You need to tell me what to cut, Foo!")
But that seems less useful than letting the parser disambiguate “What do you want to cut?” if you’ve defined it as an action applying to one thing.
“Rule for supplying a missing noun” is less for rejecting an action outright and more for automatically choosing a specific object such as a tree, or checking for a touchable thing that you might have supplied with a “cuttable” adjective, then optionally supplying a message if the rule doesn’t result in a noun.
This is the key thing for your example, I think. In order to get the rule for supplying a missing noun to fire you need:
Understand "cut" as cutting.
(This is subtle enough that the documentation example that was meant to teach it, “Four Cheeses,” originally omitted the Understand line, and wound up having the desired behavior happen through a totally different mechanism. In fact… looks like you were the one to discover that, Eleas.)