When I first gave up chemicals 10 years ago, I had no idea what to use. The organic formulas weren't really cutting it when it came to removing mascara and I just needed a clean face. That's when I first fell in love with oils.
I basically used pure Jojoba oil as a first cleanse for many years. It works to get rid of the blackest mascara and darkest smoky eye.
The downside is that it gets stuck in your eyelashes and you feel all goopy and have to go straight to sleep cause you can't really open your eyes without it being all blurry. That's a bit rough. Especially if you use coconut oil, it works, but it's so thick and really not luxe in any way. You are definitely getting back to basics if you do this.
It's moisturising and leaves a layer of oil on your skin which you then have to cleanse off. I do a proper clean with a gel cleanser after massaging Jojoba oil all over. Then I rinse the cleanser off, and wipe off excess eye makeup while my face is still wet, with a wet cotton pad. That usually gets everything but you may need to add jojoba oil to the wet cotton pad and wipe a few times.
Thankfully oil cleansers have come a long way since me just using jojoba oil. I like the Tatcha Camelia Cleansing Oil which at first I thought was pricey ($73 at Mecca), but that's for 150ml and if you were to buy 150ml of straight jojoba oil from the Jojoba Company, it would cost $60 anyway. Tatcha's Camelia Cleansing Oil cleans beautifully and doesn't leave any goop in your eyelashes, so you can see properly afterwards. Which is always a bonus, I reckon. Seeing is pretty important :)