You can use a pair of secateurs to snip snip them off at the main stem. Yeh, it will take some work. I'd advise against using chemicals. Mow them down. You just have to find the main leader and snip it at ground level, then again if it grows back.

Yep, with frequent, repeated cutting back, they will eventually give up, but that can take years with ivy. I'm normally against using chemicals, too, but in this case you might want to use a "stump and brush killer" painted onto freshly cut stumps. It won't work if too much time passes between cutting and painting, so it is best to cut and paint, cut and paint, etc.

I too would use a chemical such as SBK and paint it on the cut stumps providing they are big enough 1" in diameter of more. But how big are the stems of the ivies that you have. If they are ground cover types then digging out will be the best solution. The waxy leaf makes spraying them off with Glyphosate difficult as it will run off.

can you add a photo?

Shear brute force works best for me. Grab & yank, grab & yank. Then just dig out the main stump, not difficult with ivy. Instant gratification.

I would recommend the chemical route as ivy roots can spread a fair distance . This website explains the best times and methods for applying the chemicals. I did not look in their to products but they seem to sell in bulk for commercial growers. The same stuff is available in smaller quantities from DIY or Garden centres. https://www.progreen.co.uk/problem/ivy