Assuming you have an object called "box" and an object called "knife"...
Click on "box".
Click the Verbs tab
Click Add
For the verb, type "cut", then hit OK. You should see the "cut" verb in the list and under the Verbs tab in the left pane.
Click the "cut" verb you just created on the box object's Verbs tab (the same place you just created it)
Change "print a message" to "require another object"
Click Add under "require another object"
Select the knife object from the dropdown and click ok.
Now add whatever script you want to happen when the knife is used to cut the box.
That's it!
With the above:
> cut box with knife
You cut the box with the knife, proving the verb thingy works with "with"
If you want to see where the "with" comes in, click the "cut" Verb in the main Verbs folder under "game". The "object separator" determines what will work. So with the defaults of "with; using", both of these will work: "cut box with knife" and "cut box using knife".