Barberry, probably a seedling of Berberis thunbergii. This is considered an invasive species in some areas, including most of New England. Easiest way to get rid of it is to just dig it out but you may want to cut back a lot of the topgrowth first to avoid the thorns.

@gardengal48 (PNW Z8/9) I was unable to dig it out because its root was wedged in a middle of a rock (see first photo). Parts of the plant was producing yellow flowers and red seeds (see 2nd photo below for example). Do you think I should do anything else at this point?

What's this? · More Info

What's this? · More Info

If you don't want to apply herbicide to the stump you could cover it in a piece if thick black plastic well weighted down to exclude light from any regrowth. Leave it in place until this time next year at least.

Just out of interest the berries are edible and used in Iranian cooking. They're dried and taste quite sharp.

Oh, and it's not a vine. It's a shrub. Your example is just a bit straggly.