I use acetone, leave it in a glass jar for a couple of days (covered), then use a toothbrush to scrub away the paint. If there's still a lot, I repeat this.
When you pour the acetone in the jar and handle it, and when you remove the mini components from the jar, careful with what surfaces you are working on. If acetone spills on laminate counter-tops or floors for example, it will damage them. Do not use with plastic... if you chose to use plastic bases instead of pewter bases for example, remove the base from the mini and discard it.
After that, if it hasn't all come off, I use an ultrasonic washer/polisher with simple green and hot water (do not put acetone in it as it has a low flash point and could detonate, simple green is safe, purple stuff I am not sure but I wouldn't without research).
I do a few rounds of this and hit the mini with the toothbrush more, a needle for grooves if the paint is stubborn. Repeat as needed. I find that hot water does help with acrylic paint.