Minky is hard to sew. It's slippery, it's stretchy, you have to pin it every (max) four inches or the top layer will scrunch under the needle.
Now, there are a couple things you can do to prevent this, and I'll give you the skinny.
First let's chat about what minky actually is.
It's called Minky because it's created to imitate the fur of the Mink - a little buddy in the weasel family that was farmed for its fur. See my other blog post about that for more history. Minky nowadays is polyester. Meaning it's a petroleum product, essentially plastic, processed into stretched fibers, woven onto a base layer. It creates a sewable fake fur-like fabric.
It comes in many "fur lengths" called the 'pile'. Common pile heights are 3mm, 5mm, and 10mm. Fake fur like you see on Furry costumes is likely 15mm or more. The higher the thread-per-square-inch count, the softer the minky usually is as well.
Because it's made to imitate fur, it's messy to cut, stretchy in weird ways, and slippery as hell. Here's a few methods of How to Sew Minky without losing your mind:
Option 1
You can pin the crap out of it. 
Pin perpendicular to the edge you'll be sewing, and place pins every 3-4", the length of a credit card between each pin. I know it sounds tedious, but if you've got your magnet pin cushion next to your sewing machine, just take pins out as you sew (before the needle goes over it! Don't sew over the needle!) and you'll be roaring faster than you'd expect.
Option 2
You can iron interfacing onto the "ugly" side of the minky to make it less unruly. 
This one's tricky because fusible interfacing requires high-ish temps to melt the glue dots, in order to fuse it to the fabric. But if you use too high of a temp, you'll melt the polyester that the minky is made of. So do this at a low temp, and increase until the glue sticks and no higher, or use a cover sheet like parchment paper or thin cotton to protect the materials from the iron.
Option 3
You can buy a walking foot, and stretch needle. 
Full transparency, I used to do this. I don't anymore, because I've gotten so used to how minky moves, and what's happening in the feed dogs that I have just as much success with a regular foot now. But when I was starting my business, I definitely relied on my walking foot + stretch needle combo.
A walking foot is a big clunky thing that puts its feed-dog-like feet on the top layer as well as the built-in ones on the bottom layer, so theoretically the two layers are shimmied through together with the same pressure. It walks the fabric through.
Be sure to find out what foot fits the kind of machine you have, whether it's high-shank or low-shank, and if you're used to the lever-style clicky foot change process, instead you'll unscrew the whole presser foot head to install the walking foot with the screw.
Option 4
You can hand-baste with a needle and thread instead of using pins.
Use a needle and thread to do a normal plain running stitch instead of pinning, then just pull the hand-basted thread out when it's sewn together. The basting will keep it from scootching around while you sew.
Helpful bonus tips:
• Minky is stretchier one way than the other. If you pull the fabric side-to-side, it'll stretch quite a bit more than if you're pulling top-to-bottom. Also, it'll stretch even more diagonally. That's called the bias. The diagonal-ness. And that's important to keep in mind if you're cutting/sewing anything curved. Because your sew path will be travelling along all 3 - vertical, diagonal, horizontal - and the two pieces you're sewing together might behave differently from each other.
• Keep a hand-vacuum nearby! Minky is extremely fuzzy when you cut it, and all that fuzz needs to be vacuumed before you even pull it off the table, or it'll clog up your machine and fly up your nose. Ask me how I know.
• Minky comes in smooth and bumpy, and they behave slightly differently. So try a couple curves and straights on a swatch before you dive into your end-product fabric.