Use this on the nest. It will completely engulf it with foam and kill them quickly.
I actually found the powder is far more effective. I sprayed can after can of wasp raid to no evail. I dusted the nest with this stuff on three separate nests and they never returned to the nest. It is great because it sticks right to it.
This particular one is for ants but I believe it's the same chemical.. I think they were out of the wasp stuff at my store so they gave me this instead (but please confirm of have someone correct me on here if I am wrong). I used a water bottle with a squirt top to "poof" it onto the nest at night.
Terro T600 Ant Killer Dust,1lb https://www.amazon.com/dp/B001B1KH1Y/ref=cm_sw_r_cp_api_i_lyB8AbF56SCV9
They also seem to make some with the "poofer" already on it or you can buy one. I know pricy so I would just use a makeshift one but if it is a common problem you might want to buy it.
Easy-to-Use Pest Control Bulb Duster - Evenly Dispenses Pesticide to Get Rid of Bugs & Pests https://www.amazon.com/dp/B014V9RIFK/ref=cm_sw_r_cp_api_i_rBB8Ab1ETTHQ5
Good Luck!!
If you sprinkle some ant powder(its mostly borox ) on it and let it sit for a day or two, you might be able to drive off at least most of the ants for few days. I was having ants living in my potting media and that stuff sent them running. https://www.amazon.com/TERRO-600-1-Pound-Killer-Dust/dp/B001B1KH1Y Submerging in water might work too as another commenter mentioned but you'd have to divide first or have very large container to put it in just due to the sheer size of it. I think you should divide and place pieces all over your garden so they'll all bloom together and make a great display once established.
pest control is a good place to start, but I have used this product around my foundation and it keeps the ants away, it also seems to resist the rain and other elements washing it away. I wouldn't put it anywhere children or pets could get to it, and don't inhale it when applying!
http://www.amazon.com/TERRO-600-1-Pound-Killer-Dust/dp/B001B1KH1Y