Here, I would say that the verb is just "falling." We often use "off of" or "out of" to convey the idea of "removing."
I took the camera out of the box.
I pulled the sheets off of the bed.
I wiped the dirt off of my face.
The fan blew the smoke out of the room.
That's a fun sentence-- it was obviously designed to end with a large number of prepositional phrases. Here's another great sentence that can help you understand the way that prepositions work in English.
"It was bedtime, and a father was trying to decide which book he should read to his son. He chose a book, and asked, "would you like me to read this book?" His son said, "Ugh, no. ***What did you bring that book that I don't like to be read to out of from up for?***" "
EDIT: ninja'd by Gray :)