The optimum solution depends on which of your many resources you wish to spend.

A good sharp knife should do the trick - but it's likely that one blade isn't going to last through a bunch of carpet. Old carpet is likely to be very abrasive because of the embedded dirt, so it takes the edge off pretty quickly.

Jute or other fiber that's been soaked can develop a real resistance to being cut. It's too tough to cut, and too soft to "stand up" to the blade. A "really big pair of scissors" - i.e. tin snips, or metal-working shears may be easier (and safer) to work with. Shears get dull though, just like knives; and they also have a tendency to get loose in the joint - which lets the blades separate instead of shearing the material. You need a good (not necessarily new) pair - and you'll get some blisters using them.

The obvious solution is to find cheap labor with more time and muscle than you have, to yank the thing out for you - and if you can find help of that ilk, they can probably help you lift the furniture off so that you can just roll the stuff up without needing to cut it. Your nearby "bedbugger" (household moving company) probably has a list of "lumpers" (the guys with muscles that they hire locally to load and unload) who'd be happy to pick up a few bucks, and if it's a short job just to get it to the trash bin it shouldn't cost you more than a new Martin (not even a classic oldie). If you can find the tav' where they unwind after work, you might be able to find a couple of friendly ones that'll do it pretty cheaply.

Of course, the downside is that you may end up spending a little time with some truckers - about as painful as blisters, I suppose.

John