some greater minds and more experienced hands might have a better approach than mine, based on my removing the first of two 14" roof vents. what a pita the first one was, but based on that project, here's how I'm going to approach the second one -
first, I'd cut the caulk at the perimeter of the vent with a construction knife perpendicular to the roof, and then
go inside and after removing the inside trim, use my construction knife again, blade parallel to the roof, to cut as much as I can between the flange and the roof, and then
with the thinnest, sharpest , flexible blade putty knife I can find & sharpen, use that with a small hammer to separate the rest of the way out to the outside of the flange.
after getting the vent off, I first used a razor blade scraper, and then a 3M "stripe off wheel" to get the last of the caulk off (which worked really nicely!) see 3M Stripe Off Wheel 07499, 4 in x 5/8 in
also, and at a guess, there's probably more screws hiding under the caulk, but you should be able to locate them after removing the inside trim.
if there's a better way, I'd be happy to learn! thanks in advance for your help!