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I think if you want to remove it during a running game you have to construct an event or decision that will alter accepted cultures.

Found on reddit after some googling try this but maybe just remove the line of the culture you want to remove?
"You can change it in the files by going to history/countries and finding the country you want to change, adding a line under primary_culture that reads culture = x where x is the name of the culture as it exists in common/cultures."
 
Yep. Save editing is the easiest way to do so outside of, well, a mod. The way I would do so is to do the following (For this example I will be removing Aimara from Bolivia, but this would work with any accepted culture)
1) Open up the save game.
2) Scroll down to the country you want. I find that, since countries are so low down, the easiest way to do so is to search for the capital (in this case, capital=2313).
3) From there, go to the cultures section (ctrl + f + culture)
Code:
primary_culture="south_andean"
    culture=
    {
"quechua"
"aimara"
    }
And from there you're free to add and remove whatever you want. I don't know how the game handles junk cultures or not having 1 primary culture, but I've messed with accepted cultures a small amount and it works.
Code:
primary_culture="south_andean"
    culture=
    {
"quechua"
    }
Code:
primary_culture="south_andean"
    culture=
    {
"quechua"
"aimara"
"platinean"
"guarani"
"amazonian"
"north_andean"
"spanish"
    }
 
Recruit soldiers from culture x.

Move to tile with attrition.

Encourage soldiers in areas with said culture x

Keep military funding up so they reinforce. Boom free genocide
 
Unemployment in a region with a high percentage of cultures you don't want will encourage them to emigrate, so later, when you provide jobs once again, your primary culture is more likely to migrate there through internal emigration. Meanwhile, the US thanks you for your generosity in providing thousands of new citizens.

As said, there's always the possibility of hiring soldiers from specific pops. Any more than that strays into forum rules issues.