i am having the same problem. We happen to have a small leak during this project and the water seeped under the underlay. It was easy to remove when wet. So I got the handheld garden sprayer put water on it and kept it wet. My DH said it wasn't necessary to remove all if we use a leveler substance before we lay the new floor. I suppose it's true, but I would rather have all the old stuff up anyway.

Mikegeorge,

Get a circular saw and set the blade depth to just cut through the vinyl and underlayment. Use the saw to cut a square and then pry it up. Try for the biggest pieces you can get but with glue and staples the pieces probably won't be very big. You'll probably want a new demolition blade on your circular saw since you'll be hitting lots of fasteners.

Good Luck

Why would anyone have glued down underlayment?

Amazing.

Be aware that your vinyl tiles "may" contain asbestos. If that may be of concern to you, then have it tested. If you're going to saw through the stuff, you will create dust.