My 2 cents,
I try to attack the ivy at the root level. First I spray as much as I can with Roundup and that will knock back a whole lot of the plant. Unfortunately, you may not get rid of every single living piece of the plant, so I follow up by using a rake to pull up the weeds. Cover yourself from head to toe and use cheap leather gloves that you can dispose after using. I once pulled up over 200 feet of roots that were invading my lawn prior to planting grass seed. I obviously did not want a yard full of poison ivy. There were still a couple of small patches that I did not completely eradicate by pulling, but without the support of a huge root network, the remaining portions were easily killed off with Roundup. Typically, there will be a sort of central root somewhere in the mess. If you can isolate that portion, do so and then be relentless with the Roundup. Eventually it will completely die off. Going after Poison Ivy is not a singular battle but rather a drawn out campaign, but if you keep at it--round up and pulling roots, you will eventually win. Always cover yourself as much as possible, wash clothes afterward and shower as soon as possible. The times I have had Poison Ivy I have had to get prednisone (sp) prescriptions. That prescription will wipe out your poison ivy reaction in a couple of days and then you (or rather I was) will be more or less immune to Poison Ivy for the duration of the prescription.
If you can not pull, Round up first, wait a day or so and then mow. The herbicide should have spread to the rest of the root system by that point. You may, however, still need follow up Roundup treatments.
Best of luck to you and kill that Ivy beast!
SI2305