Do you have a heavy-good running line trimmer?? We have taken our commercial line trimmers with 0.95 line, using face shield or safety glasses and went through a bed.
It takes out about 80% to the nub. Rake out the remains......put in a bag and sell to someone for cuttings. Diquat Dibromide(Reward) is pricey so be aware. Razor Burn which is Glyophosate and Diquat combined will speed up the kill rate. Diquat is a quick contact herbicide and the gly is slower. The leaves will be effected usually in 24 hours after spraying with good kill in a week.
We run a front tine tiller after the majority of the ivy is cut down and raked out. Rake again to get the nodes and runner.........root balls too. Make sure you are aware of irrigation pipes, water lines, electrical-utility lines buried nearby--- always....!!!!!!!
After all is cleared and leveled back out, respray any shoots that should come back in a couple of weeks. You will eventually get all the ivy but it will take time.